Math1010text.log

This is XeTeX, Version 3.14159265-2.6-0.99992 (MiKTeX 2.9 64-bit) (preloaded format=xelatex 2015.11.18)  1 SEP 2016 16:13
entering extended mode
**Math1010text.tex
(Math1010text.tex
LaTeX2e <2015/01/01> patch level 2
Babel <3.9m> and hyphenation patterns for 69 languages loaded.
("C:\Program Files\MiKTeX 2.9\tex\latex\base\ifthen.sty"
Package: ifthen 2014/09/29 v1.1c Standard LaTeX ifthen package (DPC)
)
("C:\Program Files\MiKTeX 2.9\tex\latex\base\book.cls"
Document Class: book 2014/09/29 v1.4h Standard LaTeX document class
("C:\Program Files\MiKTeX 2.9\tex\latex\base\bk10.clo"
File: bk10.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
)
\c@part=\count80
\c@chapter=\count81
\c@section=\count82
\c@subsection=\count83
\c@subsubsection=\count84
\c@paragraph=\count85
\c@subparagraph=\count86
\c@figure=\count87
\c@table=\count88
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
("C:\Program Files\MiKTeX 2.9\tex\latex\pdfpages\pdfpages.sty"
Package: pdfpages 2015/09/18 v0.5d Insert pages of external PDF documents (AM)

("C:\Program Files\MiKTeX 2.9\tex\latex\tools\calc.sty"
Package: calc 2014/10/28 v4.3 Infix arithmetic (KKT,FJ)
\calc@Acount=\count89
\calc@Bcount=\count90
\calc@Adimen=\dimen103
\calc@Bdimen=\dimen104
\calc@Askip=\skip43
\calc@Bskip=\skip44
LaTeX Info: Redefining \setlength on input line 80.
LaTeX Info: Redefining \addtolength on input line 81.
\calc@Ccount=\count91
\calc@Cskip=\skip45
)
("C:\Program Files\MiKTeX 2.9\tex\latex\eso-pic\eso-pic.sty"
Package: eso-pic 2015/07/21 v2.0g eso-pic (RN)

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\atbegshi.sty"
Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO)

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\infwarerr.sty"
Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\ltxcmds.sty"
Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\ifpdf.sty"
Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO)
Package ifpdf Info: pdfTeX in PDF mode is not detected.
))
("C:\Program Files\MiKTeX 2.9\tex\latex\graphics\keyval.sty"
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
\KV@toks@=\toks14
)
("C:\Program Files\MiKTeX 2.9\tex\latex\xcolor\xcolor.sty"
Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK)

("C:\Program Files\MiKTeX 2.9\tex\latex\00miktex\color.cfg"
File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive
)
Package xcolor Info: Driver file: xetex.def on input line 225.

("C:\Program Files\MiKTeX 2.9\tex\xelatex\xetex-def\xetex.def"
File: xetex.def 2015/09/11 v4.06 LaTeX color/graphics driver for XeTeX (TeX Liv
e/RRM/JK)
)
Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337.
Package xcolor Info: Model `RGB' extended on input line 1353.
Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355.
Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356.
Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357.
Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358.
Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359.
Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360.
))
("C:\Program Files\MiKTeX 2.9\tex\latex\graphics\graphicx.sty"
Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR)

("C:\Program Files\MiKTeX 2.9\tex\latex\graphics\graphics.sty"
Package: graphics 2014/10/28 v1.0p Standard LaTeX Graphics (DPC,SPQR)

("C:\Program Files\MiKTeX 2.9\tex\latex\graphics\trig.sty"
Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
)
("C:\Program Files\MiKTeX 2.9\tex\latex\00miktex\graphics.cfg"
File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive
)
Package graphics Info: Driver file: xetex.def on input line 94.
)
\Gin@req@height=\dimen105
\Gin@req@width=\dimen106
)
\AM@pagewidth=\dimen107
\AM@pageheight=\dimen108

("C:\Program Files\MiKTeX 2.9\tex\latex\pdfpages\ppxetex.def"
File: ppxetex.def 2015/09/18 v0.5d Pdfpages driver for XeTeX (AM)
)
\AM@pagebox=\box26
\AM@toc@title=\toks15
\c@AM@survey=\count92
\AM@templatesizebox=\box27
)
("C:\Program Files\MiKTeX 2.9\tex\latex\import\import.sty"
Package: import 2009/03/23  v 5.1
)
("C:\Program Files\MiKTeX 2.9\tex\latex\tools\multicol.sty"
Package: multicol 2015/03/31 v1.8m multicolumn formatting (FMi)
\c@tracingmulticols=\count93
\mult@box=\box28
\multicol@leftmargin=\dimen109
\c@unbalance=\count94
\c@collectmore=\count95
\doublecol@number=\count96
\multicoltolerance=\count97
\multicolpretolerance=\count98
\full@width=\dimen110
\page@free=\dimen111
\premulticols=\dimen112
\postmulticols=\dimen113
\multicolsep=\skip46
\multicolbaselineskip=\skip47
\partial@page=\box29
\last@line=\box30
\maxbalancingoverflow=\dimen114
\mult@rightbox=\box31
\mult@grightbox=\box32
\mult@gfirstbox=\box33
\mult@firstbox=\box34
\@tempa=\box35
\@tempa=\box36
\@tempa=\box37
\@tempa=\box38
\@tempa=\box39
\@tempa=\box40
\@tempa=\box41
\@tempa=\box42
\@tempa=\box43
\@tempa=\box44
\@tempa=\box45
\@tempa=\box46
\@tempa=\box47
\@tempa=\box48
\@tempa=\box49
\@tempa=\box50
\@tempa=\box51
\c@columnbadness=\count99
\c@finalcolumnbadness=\count100
\last@try=\dimen115
\multicolovershoot=\dimen116
\multicolundershoot=\dimen117
\mult@nat@firstbox=\box52
\colbreak@box=\box53
\mc@col@check@num=\count101
)
("C:\Program Files\MiKTeX 2.9\tex\latex\boxedminipage\boxedminipage.sty")
("C:\Program Files\MiKTeX 2.9\tex\latex\supertabular\supertabular.sty"
Package: supertabular 2004/02/20 v4.1e the supertabular environment
\c@tracingst=\count102
\ST@wd=\dimen118
\ST@rightskip=\skip48
\ST@leftskip=\skip49
\ST@parfillskip=\skip50
\ST@pageleft=\dimen119
\ST@headht=\dimen120
\ST@tailht=\dimen121
\ST@pagesofar=\dimen122
\ST@pboxht=\dimen123
\ST@lineht=\dimen124
\ST@stretchht=\dimen125
\ST@prevht=\dimen126
\ST@toadd=\dimen127
\ST@dimen=\dimen128
\ST@pbox=\box54
)
("C:\Program Files\MiKTeX 2.9\tex\latex\tools\longtable.sty"
Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC)
\LTleft=\skip51
\LTright=\skip52
\LTpre=\skip53
\LTpost=\skip54
\LTchunksize=\count103
\LTcapwidth=\dimen129
\LT@head=\box55
\LT@firsthead=\box56
\LT@foot=\box57
\LT@lastfoot=\box58
\LT@cols=\count104
\LT@rows=\count105
\c@LT@tables=\count106
\c@LT@chunks=\count107
\LT@p@ftn=\toks16
)
("C:\Program Files\MiKTeX 2.9\tex\latex\tools\hhline.sty"
Package: hhline 2014/10/28 v2.03 Table rule package (DPC)
)
("C:\Program Files\MiKTeX 2.9\tex\latex\colortbl\colortbl.sty"
Package: colortbl 2012/02/13 v1.0a Color table columns (DPC)

("C:\Program Files\MiKTeX 2.9\tex\latex\tools\array.sty"
Package: array 2014/10/28 v2.4c Tabular extension package (FMi)
\col@sep=\dimen130
\extrarowheight=\dimen131
\NC@list=\toks17
\extratabsurround=\skip55
\backup@length=\skip56
)
\everycr=\toks18
\minrowclearance=\skip57
)
("C:\Program Files\MiKTeX 2.9\tex\latex\cancel\cancel.sty"
Package: cancel 2013/04/12 v2.2 Cancel math terms
)
(headers/Page_Size_Calculus.tex
("C:\Program Files\MiKTeX 2.9\tex\latex\geometry\geometry.sty"
Package: geometry 2010/09/12 v5.6 Page Geometry

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\ifvtex.sty"
Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO)
Package ifvtex Info: VTeX not detected.
)
("C:\Program Files\MiKTeX 2.9\tex\generic\ifxetex\ifxetex.sty"
Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
)
\Gm@cnth=\count108
\Gm@cntv=\count109
\c@Gm@tempcnt=\count110
\Gm@bindingoffset=\dimen132
\Gm@wd@mp=\dimen133
\Gm@odd@mp=\dimen134
\Gm@even@mp=\dimen135
\Gm@layoutwidth=\dimen136
\Gm@layoutheight=\dimen137
\Gm@layouthoffset=\dimen138
\Gm@layoutvoffset=\dimen139
\Gm@dimlist=\toks19

("C:\Program Files\MiKTeX 2.9\tex\xelatex\xetexconfig\geometry.cfg")))
(APEX_format.sty ("C:\Program Files\MiKTeX 2.9\tex\latex\amsmath\amsmath.sty"
Package: amsmath 2013/01/14 v2.14 AMS math features
\@mathmargin=\skip58

For additional information on amsmath, use the `?' option.
("C:\Program Files\MiKTeX 2.9\tex\latex\amsmath\amstext.sty"
Package: amstext 2000/06/29 v2.01

("C:\Program Files\MiKTeX 2.9\tex\latex\amsmath\amsgen.sty"
File: amsgen.sty 1999/11/30 v2.0
\@emptytoks=\toks20
\ex@=\dimen140
))
("C:\Program Files\MiKTeX 2.9\tex\latex\amsmath\amsbsy.sty"
Package: amsbsy 1999/11/29 v1.2d
\pmbraise@=\dimen141
)
("C:\Program Files\MiKTeX 2.9\tex\latex\amsmath\amsopn.sty"
Package: amsopn 1999/12/14 v2.01 operator names
)
\inf@bad=\count111
LaTeX Info: Redefining \frac on input line 210.
\uproot@=\count112
\leftroot@=\count113
LaTeX Info: Redefining \overline on input line 306.
\classnum@=\count114
\DOTSCASE@=\count115
LaTeX Info: Redefining \ldots on input line 378.
LaTeX Info: Redefining \dots on input line 381.
LaTeX Info: Redefining \cdots on input line 466.
\Mathstrutbox@=\box59
\strutbox@=\box60
\big@size=\dimen142
LaTeX Font Info:    Redeclaring font encoding OML on input line 566.
LaTeX Font Info:    Redeclaring font encoding OMS on input line 567.
\macc@depth=\count116
\c@MaxMatrixCols=\count117
\dotsspace@=\muskip10
\c@parentequation=\count118
\dspbrk@lvl=\count119
\tag@help=\toks21
\row@=\count120
\column@=\count121
\maxfields@=\count122
\andhelp@=\toks22
\eqnshift@=\dimen143
\alignsep@=\dimen144
\tagshift@=\dimen145
\tagwidth@=\dimen146
\totwidth@=\dimen147
\lineht@=\dimen148
\@envbody=\toks23
\multlinegap=\skip59
\multlinetaggap=\skip60
\mathdisplay@stack=\toks24
LaTeX Info: Redefining \[ on input line 2665.
LaTeX Info: Redefining \] on input line 2666.
)
("C:\Program Files\MiKTeX 2.9\tex\latex\amsfonts\amssymb.sty"
Package: amssymb 2013/01/14 v3.01 AMS font symbols

("C:\Program Files\MiKTeX 2.9\tex\latex\amsfonts\amsfonts.sty"
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
\symAMSa=\mathgroup4
\symAMSb=\mathgroup5
LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
(Font)                  U/euf/m/n --> U/euf/b/n on input line 106.
))
("C:\Program Files\MiKTeX 2.9\tex\latex\amscls\amsthm.sty"
Package: amsthm 2015/03/04 v2.20.2
\thm@style=\toks25
\thm@bodyfont=\toks26
\thm@headfont=\toks27
\thm@notefont=\toks28
\thm@headpunct=\toks29
\thm@preskip=\skip61
\thm@postskip=\skip62
\thm@headsep=\skip63
\dth@everypar=\toks30
)
("C:\Program Files\MiKTeX 2.9\tex\latex\tools\layout.sty"
Package: layout 2014/10/28 v1.2c Show layout parameters
\oneinch=\count123
\cnt@paperwidth=\count124
\cnt@paperheight=\count125
\cnt@hoffset=\count126
\cnt@voffset=\count127
\cnt@textheight=\count128
\cnt@textwidth=\count129
\cnt@topmargin=\count130
\cnt@oddsidemargin=\count131
\cnt@evensidemargin=\count132
\cnt@headheight=\count133
\cnt@headsep=\count134
\cnt@marginparsep=\count135
\cnt@marginparwidth=\count136
\cnt@marginparpush=\count137
\cnt@footskip=\count138
\fheight=\count139
\ref@top=\count140
\ref@hoffset=\count141
\ref@voffset=\count142
\ref@head=\count143
\ref@body=\count144
\ref@foot=\count145
\ref@margin=\count146
\ref@marginwidth=\count147
\ref@marginpar=\count148
\Interval=\count149
\ExtraYPos=\count150
\PositionX=\count151
\PositionY=\count152
\ArrowLength=\count153
)
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\frontendlayer\tikz.sty"
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\basiclayer\pgf.sty"
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\utilities\pgfrcs.sty"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfutil-common.tex"
\pgfutil@everybye=\toks31
\pgfutil@tempdima=\dimen149
\pgfutil@tempdimb=\dimen150

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfutil-common-lists.te
x")) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfutil-latex.def"
\pgfutil@abb=\box61
("C:\Program Files\MiKTeX 2.9\tex\latex\ms\everyshi.sty"
Package: everyshi 2001/05/15 v3.00 EveryShipout Package (MS)
))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfrcs.code.tex"
Package: pgfrcs 2015/08/07 v3.0.1a (rcs-revision 1.31)
))
Package: pgf 2015/08/07 v3.0.1a (rcs-revision 1.15)

("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\basiclayer\pgfcore.sty"
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\systemlayer\pgfsys.sty"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsys.code.tex"
Package: pgfsys 2014/07/09 v3.0.1a (rcs-revision 1.48)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfkeys.code.tex"
\pgfkeys@pathtoks=\toks32
\pgfkeys@temptoks=\toks33

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfkeysfiltered.code.te
x"
\pgfkeys@tmptoks=\toks34
))
\pgf@x=\dimen151
\pgf@y=\dimen152
\pgf@xa=\dimen153
\pgf@ya=\dimen154
\pgf@xb=\dimen155
\pgf@yb=\dimen156
\pgf@xc=\dimen157
\pgf@yc=\dimen158
\w@pgf@writea=\write3
\r@pgf@reada=\read1
\c@pgf@counta=\count154
\c@pgf@countb=\count155
\c@pgf@countc=\count156
\c@pgf@countd=\count157
\t@pgf@toka=\toks35
\t@pgf@tokb=\toks36
\t@pgf@tokc=\toks37
 ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgf.cfg"
File: pgf.cfg 2008/05/14  (rcs-revision 1.7)
)
Driver file for pgf: pgfsys-xetex.def

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsys-xetex.def"
File: pgfsys-xetex.def 2014/07/09  (rcs-revision 1.11)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsys-dvipdfmx.def"
File: pgfsys-dvipdfmx.def 2014/07/09  (rcs-revision 1.14)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsys-common-pdf.def
"
File: pgfsys-common-pdf.def 2013/10/10  (rcs-revision 1.13)
)
\pgfsys@objnum=\count158
)))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsyssoftpath.code.t
ex"
File: pgfsyssoftpath.code.tex 2013/09/09  (rcs-revision 1.9)
\pgfsyssoftpath@smallbuffer@items=\count159
\pgfsyssoftpath@bigbuffer@items=\count160
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\systemlayer\pgfsysprotocol.code.t
ex"
File: pgfsysprotocol.code.tex 2006/10/16  (rcs-revision 1.4)
)) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcore.code.tex"
Package: pgfcore 2010/04/11 v3.0.1a (rcs-revision 1.7)
 ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmath.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathcalc.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathutil.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathparser.code.tex"
\pgfmath@dimen=\dimen159
\pgfmath@count=\count161
\pgfmath@box=\box62
\pgfmath@toks=\toks38
\pgfmath@stack@operand=\toks39
\pgfmath@stack@operation=\toks40
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.basic.code.
tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.trigonometr
ic.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.random.code
.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.comparison.
code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.base.code.t
ex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.round.code.
tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.misc.code.t
ex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfunctions.integerarit
hmetics.code.tex")))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmathfloat.code.tex"
\c@pgfmathroundto@lastzeros=\count162
))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorepoints.code.tex
"
File: pgfcorepoints.code.tex 2013/10/07  (rcs-revision 1.27)
\pgf@picminx=\dimen160
\pgf@picmaxx=\dimen161
\pgf@picminy=\dimen162
\pgf@picmaxy=\dimen163
\pgf@pathminx=\dimen164
\pgf@pathmaxx=\dimen165
\pgf@pathminy=\dimen166
\pgf@pathmaxy=\dimen167
\pgf@xx=\dimen168
\pgf@xy=\dimen169
\pgf@yx=\dimen170
\pgf@yy=\dimen171
\pgf@zx=\dimen172
\pgf@zy=\dimen173
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorepathconstruct.c
ode.tex"
File: pgfcorepathconstruct.code.tex 2013/10/07  (rcs-revision 1.29)
\pgf@path@lastx=\dimen174
\pgf@path@lasty=\dimen175
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorepathusage.code.
tex"
File: pgfcorepathusage.code.tex 2014/11/02  (rcs-revision 1.24)
\pgf@shorten@end@additional=\dimen176
\pgf@shorten@start@additional=\dimen177
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorescopes.code.tex
"
File: pgfcorescopes.code.tex 2015/05/08  (rcs-revision 1.46)
\pgfpic=\box63
\pgf@hbox=\box64
\pgf@layerbox@main=\box65
\pgf@picture@serial@count=\count163
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoregraphicstate.co
de.tex"
File: pgfcoregraphicstate.code.tex 2014/11/02  (rcs-revision 1.12)
\pgflinewidth=\dimen178
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoretransformations
.code.tex"
File: pgfcoretransformations.code.tex 2015/08/07  (rcs-revision 1.20)
\pgf@pt@x=\dimen179
\pgf@pt@y=\dimen180
\pgf@pt@temp=\dimen181
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorequick.code.tex"
File: pgfcorequick.code.tex 2008/10/09  (rcs-revision 1.3)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoreobjects.code.te
x"
File: pgfcoreobjects.code.tex 2006/10/11  (rcs-revision 1.2)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorepathprocessing.
code.tex"
File: pgfcorepathprocessing.code.tex 2013/09/09  (rcs-revision 1.9)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorearrows.code.tex
"
File: pgfcorearrows.code.tex 2015/05/14  (rcs-revision 1.43)
\pgfarrowsep=\dimen182
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoreshade.code.tex"
File: pgfcoreshade.code.tex 2013/07/15  (rcs-revision 1.15)
\pgf@max=\dimen183
\pgf@sys@shading@range@num=\count164
) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoreimage.code.te
x"
File: pgfcoreimage.code.tex 2013/07/15  (rcs-revision 1.18)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoreexternal.code.t
ex"
File: pgfcoreexternal.code.tex 2014/07/09  (rcs-revision 1.21)
\pgfexternal@startupbox=\box66
))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorelayers.code.tex
"
File: pgfcorelayers.code.tex 2013/07/18  (rcs-revision 1.7)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcoretransparency.co
de.tex"
File: pgfcoretransparency.code.tex 2013/09/30  (rcs-revision 1.5)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\basiclayer\pgfcorepatterns.code.t
ex"
File: pgfcorepatterns.code.tex 2013/11/07  (rcs-revision 1.5)
)))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\modules\pgfmoduleshapes.code.tex"
File: pgfmoduleshapes.code.tex 2014/03/21  (rcs-revision 1.35)
\pgfnodeparttextbox=\box67
) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\modules\pgfmoduleplot.code.tex"
File: pgfmoduleplot.code.tex 2015/08/03  (rcs-revision 1.13)
)
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\compatibility\pgfcomp-version-0-65.
sty"
Package: pgfcomp-version-0-65 2007/07/03 v3.0.1a (rcs-revision 1.7)
\pgf@nodesepstart=\dimen184
\pgf@nodesepend=\dimen185
)
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\compatibility\pgfcomp-version-1-18.
sty"
Package: pgfcomp-version-1-18 2007/07/23 v3.0.1a (rcs-revision 1.1)
)) ("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\utilities\pgffor.sty"
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\utilities\pgfkeys.sty"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgfkeys.code.tex"))
("C:\Program Files\MiKTeX 2.9\tex\latex\pgf\math\pgfmath.sty"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmath.code.tex"))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\utilities\pgffor.code.tex"
Package: pgffor 2013/12/13 v3.0.1a (rcs-revision 1.25)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\math\pgfmath.code.tex")
\pgffor@iter=\dimen186
\pgffor@skip=\dimen187
\pgffor@stack=\toks41
\pgffor@toks=\toks42
))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\tikz.code.tex"
Package: tikz 2015/08/07 v3.0.1a (rcs-revision 1.151)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\libraries\pgflibraryplothandlers.
code.tex"
File: pgflibraryplothandlers.code.tex 2013/08/31 v3.0.1a (rcs-revision 1.20)
\pgf@plot@mark@count=\count165
\pgfplotmarksize=\dimen188
)
\tikz@lastx=\dimen189
\tikz@lasty=\dimen190
\tikz@lastxsaved=\dimen191
\tikz@lastysaved=\dimen192
\tikzleveldistance=\dimen193
\tikzsiblingdistance=\dimen194
\tikz@figbox=\box68
\tikz@figbox@bg=\box69
\tikz@tempbox=\box70
\tikz@tempbox@bg=\box71
\tikztreelevel=\count166
\tikznumberofchildren=\count167
\tikznumberofcurrentchild=\count168
\tikz@fig@count=\count169

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\modules\pgfmodulematrix.code.tex"
File: pgfmodulematrix.code.tex 2013/09/17  (rcs-revision 1.8)
\pgfmatrixcurrentrow=\count170
\pgfmatrixcurrentcolumn=\count171
\pgf@matrix@numberofcolumns=\count172
)
\tikz@expandcount=\count173

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
librarytopaths.code.tex"
File: tikzlibrarytopaths.code.tex 2008/06/17 v3.0.1a (rcs-revision 1.2)
)))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
librarycalc.code.tex"
File: tikzlibrarycalc.code.tex 2013/07/15 v3.0.1a (rcs-revision 1.9)
) ("C:\Program Files\MiKTeX 2.9\tex\latex\base\makeidx.sty"
Package: makeidx 2014/09/29 v1.0m Standard LaTeX package
) ("C:\Program Files\MiKTeX 2.9\tex\latex\media9\media9.sty"
("C:\Program Files\MiKTeX 2.9\tex\latex\l3kernel\expl3.sty"
Package: expl3 2015/11/04 v6224 L3 programming layer (loader) 

("C:\Program Files\MiKTeX 2.9\tex\latex\l3kernel\expl3-code.tex"
Package: expl3 2015/11/04 v6224 L3 programming layer (code) 
L3 Module: l3bootstrap 2015/10/18 v6213 L3 Bootstrap code
L3 Module: l3names 2015/11/03 v6220 L3 Namespace for primitives
L3 Module: l3basics 2015/09/22 v6033 L3 Basic definitions
L3 Module: l3expan 2015/09/10 v5983 L3 Argument expansion
L3 Module: l3tl 2015/09/29 v6121 L3 Token lists
L3 Module: l3str 2015/09/20 v6021 L3 Strings
L3 Module: l3seq 2015/08/05 v5777 L3 Sequences and stacks
L3 Module: l3int 2015/09/25 v6089 L3 Integers
\c_max_int=\count174
\l_tmpa_int=\count175
\l_tmpb_int=\count176
\g_tmpa_int=\count177
\g_tmpb_int=\count178
L3 Module: l3quark 2015/08/17 v5855 L3 Quarks
L3 Module: l3prg 2015/11/01 v6216 L3 Control structures
\g__prg_map_int=\count179
L3 Module: l3clist 2015/09/02 v5901 L3 Comma separated lists
L3 Module: l3token 2015/09/28 v6114 L3 Experimental token manipulation
L3 Module: l3prop 2015/08/05 v5777 L3 Property lists
L3 Module: l3msg 2015/09/28 v6113 L3 Messages
L3 Module: l3file 2015/09/23 v6037 L3 File and I/O operations
\l_iow_line_count_int=\count180
\l__iow_target_count_int=\count181
\l__iow_current_line_int=\count182
\l__iow_current_word_int=\count183
\l__iow_current_indentation_int=\count184
L3 Module: l3skip 2015/09/25 v6089 L3 Dimensions and skips
\c_zero_dim=\dimen195
\c_max_dim=\dimen196
\l_tmpa_dim=\dimen197
\l_tmpb_dim=\dimen198
\g_tmpa_dim=\dimen199
\g_tmpb_dim=\dimen200
\c_zero_skip=\skip64
\c_max_skip=\skip65
\l_tmpa_skip=\skip66
\l_tmpb_skip=\skip67
\g_tmpa_skip=\skip68
\g_tmpb_skip=\skip69
\c_zero_muskip=\muskip11
\c_max_muskip=\muskip12
\l_tmpa_muskip=\muskip13
\l_tmpb_muskip=\muskip14
\g_tmpa_muskip=\muskip15
\g_tmpb_muskip=\muskip16
L3 Module: l3keys 2015/09/23 v6037 L3 Key-value interfaces
\g__keyval_level_int=\count185
\l_keys_choice_int=\count186
L3 Module: l3fp 2015/08/25 v5890 L3 Floating points
\c__fp_leading_shift_int=\count187
\c__fp_middle_shift_int=\count188
\c__fp_trailing_shift_int=\count189
\c__fp_big_leading_shift_int=\count190
\c__fp_big_middle_shift_int=\count191
\c__fp_big_trailing_shift_int=\count192
\c__fp_Bigg_leading_shift_int=\count193
\c__fp_Bigg_middle_shift_int=\count194
\c__fp_Bigg_trailing_shift_int=\count195
L3 Module: l3box 2015/08/09 v5822 L3 Experimental boxes
\c_empty_box=\box72
\l_tmpa_box=\box73
\l_tmpb_box=\box74
\g_tmpa_box=\box75
\g_tmpb_box=\box76
L3 Module: l3coffins 2015/08/06 v5789 L3 Coffin code layer
\l__coffin_internal_box=\box77
\l__coffin_internal_dim=\dimen201
\l__coffin_offset_x_dim=\dimen202
\l__coffin_offset_y_dim=\dimen203
\l__coffin_x_dim=\dimen204
\l__coffin_y_dim=\dimen205
\l__coffin_x_prime_dim=\dimen206
\l__coffin_y_prime_dim=\dimen207
\c_empty_coffin=\box78
\l__coffin_aligned_coffin=\box79
\l__coffin_aligned_internal_coffin=\box80
\l_tmpa_coffin=\box81
\l_tmpb_coffin=\box82
\l__coffin_display_coffin=\box83
\l__coffin_display_coord_coffin=\box84
\l__coffin_display_pole_coffin=\box85
\l__coffin_display_offset_dim=\dimen208
\l__coffin_display_x_dim=\dimen209
\l__coffin_display_y_dim=\dimen210
L3 Module: l3color 2014/08/23 v5354 L3 Experimental color support
L3 Module: l3candidates 2015/11/01 v6216 L3 Experimental additions to l3kernel
\l__box_top_dim=\dimen211
\l__box_bottom_dim=\dimen212
\l__box_left_dim=\dimen213
\l__box_right_dim=\dimen214
\l__box_top_new_dim=\dimen215
\l__box_bottom_new_dim=\dimen216
\l__box_left_new_dim=\dimen217
\l__box_right_new_dim=\dimen218
\l__box_internal_box=\box86
\l__coffin_bounding_shift_dim=\dimen219
\l__coffin_left_corner_dim=\dimen220
\l__coffin_right_corner_dim=\dimen221
\l__coffin_bottom_corner_dim=\dimen222
\l__coffin_top_corner_dim=\dimen223
\l__coffin_scaled_total_height_dim=\dimen224
\l__coffin_scaled_width_dim=\dimen225
L3 Module: l3sys 2015/09/25 v6087 L3 Experimental system/runtime functions
L3 Module: l3luatex 2015/09/10 v5983 L3 Experimental LuaTeX-specific functions
)
("C:\Program Files\MiKTeX 2.9\tex\latex\l3kernel\l3unicode-data.def"
File: l3unicode-data.def 2015/07/20 v5676 L3 Unicode data
)
("C:\Program Files\MiKTeX 2.9\tex\latex\l3kernel\l3xdvipdfmx.def"
File: l3xdvidpfmx.def 2015/09/10 v5983 L3 Experimental driver: xdvipdfmx
))
("C:\Program Files\MiKTeX 2.9\tex\latex\l3experimental\l3str\l3regex.sty"
Package: l3regex 2015/11/04 v6224 L3 Experimental regular expressions

("C:\Program Files\MiKTeX 2.9\tex\latex\l3experimental\l3str\l3tl-build.sty"
Package: l3tl-build 2015/11/04 v6224 L3 Experimental token list construction
\l__tl_build_start_index_int=\count196
\l__tl_build_index_int=\count197
)
("C:\Program Files\MiKTeX 2.9\tex\latex\l3experimental\l3str\l3tl-analysis.sty"
Package: l3tl-analysis 2015/09/26 v6106 L3 Experimental token lists analysis
\l__tl_analysis_normal_int=\count198
\l__tl_analysis_index_int=\count199
\l__tl_analysis_nesting_int=\count200
\l__tl_analysis_type_int=\count201
) ("C:\Program Files\MiKTeX 2.9\tex\latex\l3experimental\l3str\l3flag.sty"
Package: l3flag 2015/11/04 v6224 L3 Experimental flags
)
("C:\Program Files\MiKTeX 2.9\tex\latex\l3experimental\l3str\l3str-convert.sty"
Package: l3str-convert 2015/09/26 v6106 L3 Experimental string encoding convers
ions
\l__str_internal_int=\count202
)
\l__regex_internal_a_int=\count203
\l__regex_internal_b_int=\count204
\l__regex_internal_c_int=\count205
\l__regex_balance_int=\count206
\l__regex_group_level_int=\count207
\l__regex_mode_int=\count208
\l__regex_catcodes_int=\count209
\l__regex_default_catcodes_int=\count210
\c__regex_catcode_L_int=\count211
\c__regex_catcode_O_int=\count212
\c__regex_catcode_A_int=\count213
\c__regex_all_catcodes_int=\count214
\l__regex_show_lines_int=\count215
\l__regex_min_state_int=\count216
\l__regex_max_state_int=\count217
\l__regex_left_state_int=\count218
\l__regex_right_state_int=\count219
\l__regex_capturing_group_int=\count220
\l__regex_min_pos_int=\count221
\l__regex_max_pos_int=\count222
\l__regex_current_pos_int=\count223
\l__regex_start_pos_int=\count224
\l__regex_success_pos_int=\count225
\l__regex_current_char_int=\count226
\l__regex_current_catcode_int=\count227
\l__regex_last_char_int=\count228
\l__regex_case_changed_char_int=\count229
\l__regex_current_state_int=\count230
\l__regex_step_int=\count231
\l__regex_min_active_int=\count232
\l__regex_max_active_int=\count233
\l__regex_replacement_csnames_int=\count266
\l__regex_match_count_int=\count267
\l__regex_submatch_int=\count268
\l__regex_zeroth_submatch_int=\count269
) ("C:\Program Files\MiKTeX 2.9\tex\latex\l3packages\l3keys2e\l3keys2e.sty"
Package: l3keys2e 2015/11/04 v6224 LaTeX2e option processing using LaTeX3 keys
)
("C:\Program Files\MiKTeX 2.9\tex\latex\l3packages\xparse\xparse.sty"
Package: xparse 2015/11/04 v6224 L3 Experimental document command parser
\l__xparse_current_arg_int=\count270
\l__xparse_m_args_int=\count271
\l__xparse_mandatory_args_int=\count272
\l__xparse_processor_int=\count273
\l__xparse_v_nesting_int=\count274
)
("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\atenddvi.sty"
Package: atenddvi 2007/04/17 v1.1 At end DVI hook (HO)

("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\zref-abspage.sty"
Package: zref-abspage 2012/04/04 v2.24 Module abspage for zref (HO)

("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\zref-base.sty"
Package: zref-base 2012/04/04 v2.24 Module base for zref (HO)

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\kvsetkeys.sty"
Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO)

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\etexcmds.sty"
Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\ifluatex.sty"
Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO)
Package ifluatex Info: LuaTeX not detected.
)
Package etexcmds Info: Could not find \expanded.
(etexcmds)             That can mean that you are not using pdfTeX 1.50 or
(etexcmds)             that some package has redefined \expanded.
(etexcmds)             In the latter case, load this package earlier.
))
("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\kvdefinekeys.sty"
Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\pdftexcmds.sty"
Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO
)
Package pdftexcmds Info: LuaTeX not detected.
Package pdftexcmds Info: pdfTeX >= 1.30 not detected.
Package pdftexcmds Info: \pdf@primitive is available.
Package pdftexcmds Info: \pdf@ifprimitive is available.
Package pdftexcmds Info: \pdfdraftmode not found.
)
("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\auxhook.sty"
Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO)
)
Package zref Info: New property list: main on input line 759.
Package zref Info: New property: default on input line 760.
Package zref Info: New property: page on input line 761.
)
\c@abspage=\count275
Package zref Info: New property: abspage on input line 62.
)
("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\zref-lastpage.sty"
Package: zref-lastpage 2012/04/04 v2.24 Module lastpage for zref (HO)

("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\atveryend.sty"
Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO)
Package atveryend Info: \enddocument detected (standard20110627).
)
Package zref Info: New property list: LastPage on input line 55.
))
Package: media9 2015/11/02 v0.60 acrobat-9/X compatible media
\g_mix_pkgresizeflag_int=\count276

("C:\Program Files\MiKTeX 2.9\tex\latex\media9\pdfbase.sty"
Package: pdfbase 2015/11/02 v0.2 driver independent access to low-level PDF fea
tures
\g_pbs_obj_int=\count277
\g_pbs_oc_int=\count278
)
("C:\Program Files\MiKTeX 2.9\tex\latex\ocgx2\ocgbase.sty"
Package: ocgbase 2015/11/02 v0.2 support package for ocgx2.sty
)
\l_mix_poster_box=\box87
\g_mix_wd_dim=\dimen226
\g_mix_ht_dim=\dimen227
\g_mix_dp_dim=\dimen228
\g_mix_rmcnt_int=\count279
\l_mix_viewcnt_int=\count280
\g@mix@page@int=\count281
\g_mix_resizeflag_int=\count282
\l_mix_lineno_int=\count283
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \addmediapath with sig. 'm' on line 838.
.................................................
\l_mix_pbtn_box=\box88
\mix@btn@dim=\dimen229
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \includemedia with sig. 'O{}mm' on line 1226.
.................................................
\g_mix_mbtncnt_int=\count284
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \mediabutton with sig. 'O{}m' on line 2433.
.................................................
)
("C:\Program Files\MiKTeX 2.9\tex\latex\changepage\changepage.sty"
Package: changepage 2009/10/20 v1.0c check page and change page layout
\c@cp@cntr=\count285
\cp@tempcnt=\count286
)
("C:\Program Files\MiKTeX 2.9\tex\latex\ulem\ulem.sty"
\UL@box=\box89
\UL@hyphenbox=\box90
\UL@skip=\skip70
\UL@hook=\toks43
\UL@height=\dimen230
\UL@pe=\count287
\UL@pixel=\dimen231
\ULC@box=\box91
Requested font "lasy6" scaled 1000
Package: ulem 2012/05/18
\ULdepth=\dimen232
)
("C:\Program Files\MiKTeX 2.9\tex\latex\hyperref\hyperref.sty"
Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\hobsub-hyperref.sty"
Package: hobsub-hyperref 2012/04/25 v1.12 Bundle oberdiek, subset hyperref (HO)


("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\hobsub-generic.sty"
Package: hobsub-generic 2012/04/25 v1.12 Bundle oberdiek, subset generic (HO)
Package: hobsub 2012/04/25 v1.12 Construct package bundles (HO)
Package hobsub Info: Skipping package `infwarerr' (already loaded).
Package hobsub Info: Skipping package `ltxcmds' (already loaded).
Package hobsub Info: Skipping package `ifluatex' (already loaded).
Package hobsub Info: Skipping package `ifvtex' (already loaded).
Package: intcalc 2007/09/27 v1.1 Expandable calculations with integers (HO)
Package hobsub Info: Skipping package `ifpdf' (already loaded).
Package hobsub Info: Skipping package `etexcmds' (already loaded).
Package hobsub Info: Skipping package `kvsetkeys' (already loaded).
Package hobsub Info: Skipping package `kvdefinekeys' (already loaded).
Package hobsub Info: Skipping package `pdftexcmds' (already loaded).
Package: pdfescape 2011/11/25 v1.13 Implements pdfTeX's escape features (HO)
Package: bigintcalc 2012/04/08 v1.3 Expandable calculations on big integers (HO
)
Package: bitset 2011/01/30 v1.1 Handle bit-vector datatype (HO)
Package: uniquecounter 2011/01/30 v1.2 Provide unlimited unique counter (HO)
)
Package hobsub Info: Skipping package `hobsub' (already loaded).
Package: letltxmacro 2010/09/02 v1.4 Let assignment for LaTeX macros (HO)
Package: hopatch 2011/06/24 v1.1 Wrapper for package hooks (HO)
Package: xcolor-patch 2011/01/30 xcolor patch
Package hobsub Info: Skipping package `atveryend' (already loaded).
Package hobsub Info: Skipping package `atbegshi' (already loaded).
Package: refcount 2011/10/16 v3.4 Data extraction from label references (HO)
Package: hycolor 2011/01/30 v1.7 Color options for hyperref/bookmark (HO)
)
("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\kvoptions.sty"
Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO)
)
\@linkdim=\dimen233
\Hy@linkcounter=\count288
\Hy@pagecounter=\count289

("C:\Program Files\MiKTeX 2.9\tex\latex\hyperref\pd1enc.def"
File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO)
)
\Hy@SavedSpaceFactor=\count290

("C:\Program Files\MiKTeX 2.9\tex\latex\00miktex\hyperref.cfg"
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
)
Package hyperref Info: Option `bookmarksnumbered' set `true' on input line 4319
.
Package hyperref Info: Hyper figures OFF on input line 4443.
Package hyperref Info: Link nesting OFF on input line 4448.
Package hyperref Info: Hyper index ON on input line 4451.
Package hyperref Info: Plain pages OFF on input line 4458.
Package hyperref Info: Backreferencing OFF on input line 4463.
Package hyperref Info: Implicit mode ON; LaTeX internals redefined.
Package hyperref Info: Bookmarks ON on input line 4688.
\c@Hy@tempcnt=\count291

("C:\Program Files\MiKTeX 2.9\tex\latex\url\url.sty"
\Urlmuskip=\muskip17
Package: url 2013/09/16  ver 3.4  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 5041.
\XeTeXLinkMargin=\dimen256
Requested font "pzdr" at 0.00002pt
\Fld@menulength=\count292
\Field@Width=\dimen257
\Fld@charsize=\dimen258
Package hyperref Info: Hyper figures OFF on input line 6295.
Package hyperref Info: Link nesting OFF on input line 6300.
Package hyperref Info: Hyper index ON on input line 6303.
Package hyperref Info: backreferencing OFF on input line 6310.
Package hyperref Info: Link coloring OFF on input line 6315.
Package hyperref Info: Link coloring with OCG OFF on input line 6320.
Package hyperref Info: PDF/A mode OFF on input line 6325.
LaTeX Info: Redefining \ref on input line 6365.
LaTeX Info: Redefining \pageref on input line 6369.
\Hy@abspage=\count293
\c@Item=\count294
\c@Hfootnote=\count295
)

Package hyperref Message: Driver (autodetected): hxetex.

("C:\Program Files\MiKTeX 2.9\tex\latex\hyperref\hxetex.def"
File: hxetex.def 2012/11/06 v6.83m Hyperref driver for XeTeX

("C:\Program Files\MiKTeX 2.9\tex\latex\hyperref\puenc.def"
File: puenc.def 2012/11/06 v6.83m Hyperref: PDF Unicode definition (HO)
)
("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\stringenc.sty"
Package: stringenc 2011/12/02 v1.10 Convert strings between diff. encodings (HO
)
)
\pdfm@box=\box92
\c@Hy@AnnotLevel=\count296
\HyField@AnnotCount=\count297
\Fld@listcount=\count298
\c@bookmark@seq@number=\count299

("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\rerunfilecheck.sty"
Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO)
Package rerunfilecheck Info: Feature \pdfmdfivesum is not available
(rerunfilecheck)             (e.g. pdfTeX or LuaTeX with package `pdftexcmds').

(rerunfilecheck)             Therefore file contents cannot be checked efficien
tly
(rerunfilecheck)             and the loading of the package is aborted.
)
\Hy@SectionHShift=\skip71
)
("C:\Program Files\MiKTeX 2.9\tex\latex\enumitem\enumitem.sty"
Package: enumitem 2011/09/28 v3.5.2 Customized lists
\labelindent=\skip72
\enit@outerparindent=\dimen259
\enit@toks=\toks44
\enit@inbox=\box93
\enitdp@description=\count300
)
("C:\Program Files\MiKTeX 2.9\tex\latex\esvect\esvect.sty"
Package: esvect 
\symesvector=\mathgroup6
LaTeX Font Info:    Redeclaring math symbol \fldr on input line 38.
)
\@indexfile=\write4

Writing index file Math1010text.idx
\topmarginlength=\skip73
\bottommarginlength=\skip74
\oddpagemarginlength=\skip75
\evenpagemarginlength=\skip76
\marginlinelength=\skip77
\c@examplecounter=\count301
\specialboxlength=\skip78
\specialboxtitlelength=\skip79
\specialboxinnerseplength=\skip80
\specialboxinnerseplengthx=\skip81
\specialboxinnerseplengthy=\skip82
\c@definitioncounter=\count302
\c@theoremcounter=\count303
\c@keyideacounter=\count304
\showexercises=\count305
\numberofexercises=\count306
\c@numofexer=\count307
\c@negnumofexer=\count308
\c@debug=\count309
\c@exercisecounter=\count310
\c@IMTcount=\count311
\c@IMTcount_temp=\count312
\exread=\read2
\exsetread=\read3
\exansread=\read4
\printansread=\read5
\answrite=\write5
) (headers/Header_Calculus.tex
("C:\Program Files\MiKTeX 2.9\tex\latex\fancyhdr\fancyhdr.sty"
\fancy@headwidth=\skip83
\f@ncyO@elh=\skip84
\f@ncyO@erh=\skip85
\f@ncyO@olh=\skip86
\f@ncyO@orh=\skip87
\f@ncyO@elf=\skip88
\f@ncyO@erf=\skip89
\f@ncyO@olf=\skip90
\f@ncyO@orf=\skip91
)
("C:\Program Files\MiKTeX 2.9\tex\latex\lipsum\lipsum.sty"
Package: lipsum 2014/07/27 v1.3 150 paragraphs of Lorem Ipsum dummy text
\c@lips@count=\count313
)
("C:\Program Files\MiKTeX 2.9\tex\latex\units\units.sty"
Package: units 1998/08/04 v0.9b Typesetting units

("C:\Program Files\MiKTeX 2.9\tex\latex\units\nicefrac.sty"
Package: nicefrac 1998/08/04 v0.9b Nice fractions
\L@UnitsRaiseDisplaystyle=\skip92
\L@UnitsRaiseTextstyle=\skip93
\L@UnitsRaiseScriptstyle=\skip94
))
("C:\Program Files\MiKTeX 2.9\tex\latex\caption\caption.sty"
Package: caption 2015/09/17 v3.3-111 Customizing captions (AR)

("C:\Program Files\MiKTeX 2.9\tex\latex\caption\caption3.sty"
Package: caption3 2015/09/20 v1.7-115 caption3 kernel (AR)
Package caption3 Info: TeX engine: e-TeX on input line 57.
\captionmargin=\dimen260
\captionmargin@=\dimen261
\captionwidth=\dimen262
\caption@tempdima=\dimen263
\caption@indent=\dimen264
\caption@parindent=\dimen265
\caption@hangindent=\dimen266
)
\c@ContinuedFloat=\count314
Package caption Info: hyperref package is loaded.
Package caption Info: longtable package is loaded.

("C:\Program Files\MiKTeX 2.9\tex\latex\caption\ltcaption.sty"
Package: ltcaption 2013/06/09 v1.4-94 longtable captions (AR)
)
Package caption Info: supertabular package is loaded.
)
\titleheight=\dimen267
\c@myfigurecounter=\count315
)
("C:\Program Files\MiKTeX 2.9\tex\latex\pgfplots\pgfplots.sty"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.revision.tex")
Package: pgfplots 2015/05/02 v1.12.1 Data Visualization (1.12.1)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotscore.code.tex"
\t@pgfplots@toka=\toks45
\t@pgfplots@tokb=\toks46
\t@pgfplots@tokc=\toks47
\pgfplots@tmpa=\dimen268
\c@pgfplots@coordindex=\count316
\c@pgfplots@scanlineindex=\count317

("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\sys\pgfplotssysgeneric.code.
tex"))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\libs\pgfplotslibrary.code.te
x")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\oldpgfcompatib\pgfplotsoldpg
fsupp_loader.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\libraries\pgflibraryfpu.code.tex"
)) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotsutil.code.te
x"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\liststructure\pgfplotslistst
ructure.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\liststructure\pgfplotslistst
ructureext.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\liststructure\pgfplotsarray.
code.tex"
\c@pgfplotsarray@tmp=\count318
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\liststructure\pgfplotsmatrix
.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\numtable\pgfplotstableshared
.code.tex"
\c@pgfplotstable@counta=\count319
\t@pgfplotstable@a=\toks48
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\liststructure\pgfplotsdeque.
code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotsbinary.code.tex
"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotsbinary.data.cod
e.tex"))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotsutil.verb.code.
tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\libs\pgflibrarypgfplots.surf
shading.code.tex"
\c@pgfplotslibrarysurf@no=\count320

("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\sys\pgflibrarypgfplots.surfs
hading.pgfsys-xetex.def"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\sys\pgflibrarypgfplots.surfs
hading.pgfsys-dvipdfmx.def"
\c@pgfplotslibrarysurf@streamlen=\count321
))))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotscolormap.code.t
ex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\util\pgfplotscolor.code.tex"
))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotsstackedplots.code.te
x")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotsplothandlers.code.te
x"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotsmeshplothandler.code
.tex"))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.scaling.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotscoordprocessing.code
.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.errorbars.code.tex"
) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.markers.code.tex"
) ("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplotsticks.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgfplots\pgfplots.paths.code.tex")
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
librarydecorations.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\modules\pgfmoduledecorations.code
.tex"
\pgfdecoratedcompleteddistance=\dimen269
\pgfdecoratedremainingdistance=\dimen270
\pgfdecoratedinputsegmentcompleteddistance=\dimen271
\pgfdecoratedinputsegmentremainingdistance=\dimen272
\pgf@decorate@distancetomove=\dimen273
\pgf@decorate@repeatstate=\count322
\pgfdecorationsegmentamplitude=\dimen274
\pgfdecorationsegmentlength=\dimen275
)
\tikz@lib@dec@box=\box94
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
librarydecorations.pathmorphing.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\libraries\decorations\pgflibraryd
ecorations.pathmorphing.code.tex"))
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
librarydecorations.pathreplacing.code.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\libraries\decorations\pgflibraryd
ecorations.pathreplacing.code.tex"))
\pgfplots@numplots=\count323
\pgfplots@xmin@reg=\dimen276
\pgfplots@xmax@reg=\dimen277
\pgfplots@ymin@reg=\dimen278
\pgfplots@ymax@reg=\dimen279
\pgfplots@zmin@reg=\dimen280
\pgfplots@zmax@reg=\dimen281
)
("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\frontendlayer\tikz\libraries\tikz
libraryplotmarks.code.tex"
File: tikzlibraryplotmarks.code.tex 2008/01/09 v3.0.1a (rcs-revision 1.1)

("C:\Program Files\MiKTeX 2.9\tex\generic\pgf\libraries\pgflibraryplotmarks.cod
e.tex"
File: pgflibraryplotmarks.code.tex 2015/08/03 v3.0.1a (rcs-revision 1.14)
)))
Requested font "cmss10" at 10.0pt
 ("C:\Program Files\MiKTeX 2.9\tex\xelatex\mathspec\mathspec.sty"
Package: mathspec 2009/09/30 v0.2 LaTeX Package (Mathematics font selection for
 XeLaTeX)

("C:\Program Files\MiKTeX 2.9\tex\latex\etoolbox\etoolbox.sty"
Package: etoolbox 2015/08/02 v2.2a e-TeX tools for LaTeX (JAW)
\etb@tempcnta=\count324
)
("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec.sty"
Package: fontspec 2015/07/22 v2.4d Font selection for XeLaTeX and LuaLaTeX
\l_fontspec_script_int=\count325
\l_fontspec_language_int=\count326
\l_fontspec_strnum_int=\count327
\l__fontspec_tmpa_dim=\dimen282
\l__fontspec_tmpb_dim=\dimen283
\l__fontspec_tmpc_dim=\dimen284

("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec-patches.sty"
Package: fontspec-patches 2015/07/22 v2.4d Font selection for XeLaTeX and LuaLa
TeX
LaTeX Info: Redefining \em on input line 49.
LaTeX Info: Redefining \emph on input line 57.
LaTeX Info: Redefining \- on input line 60.
.................................................
. LaTeX info: "xparse/redefine-command"
. 
. Redefining command \oldstylenums with sig. 'm' on line 155.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \liningnums with sig. 'm' on line 159.
.................................................
)
("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec-xetex.sty"
Package: fontspec-xetex 2015/07/22 v2.4d Font selection for XeLaTeX and LuaLaTe
X

("C:\Program Files\MiKTeX 2.9\tex\latex\base\fontenc.sty"
Package: fontenc 2005/09/27 v1.99g Standard LaTeX package

("C:\Program Files\MiKTeX 2.9\tex\latex\euenc\eu1enc.def"
File: eu1enc.def 2010/05/27 v0.1h Experimental Unicode font encodings
)
LaTeX Font Info:    Try loading font information for EU1+lmr on input line 105.


("C:\Program Files\MiKTeX 2.9\tex\latex\euenc\eu1lmr.fd"
File: eu1lmr.fd 2009/10/30 v1.6 Font defs for Latin Modern
)
Requested font "[lmroman10-regular]:mapping=tex-text" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmroman10-regular.otf
)
("C:\Program Files\MiKTeX 2.9\tex\xelatex\xunicode\xunicode.sty"
File: xunicode.sty 2011/09/09 v0.981 provides access to latin accents and many 
other characters in Unicode lower plane

("C:\Program Files\MiKTeX 2.9\tex\latex\tipa\t3enc.def"
File: t3enc.def 2001/12/31 T3 encoding
Requested font "[lmromanslant10-regular]:mapping=tex-text" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmromanslant10-regular
.otf
Requested font "[lmroman10-italic]:mapping=tex-text" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmroman10-italic.otf
Requested font "[lmroman10-bold]:mapping=tex-text" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmroman10-bold.otf
LaTeX Font Info:    Try loading font information for EU1+lmss on input line 357
.

("C:\Program Files\MiKTeX 2.9\tex\latex\euenc\eu1lmss.fd"
File: eu1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern
)
Requested font "[lmsans10-regular]:mapping=tex-text" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmsans10-regular.otf
)
\tipaTiiicode=\count328
\tipasavetokens=\toks49
\tipachecktokens=\toks50
)
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \__fontspec_post_arg:w with sig. 'mmO{}' on line 42.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \fontspec with sig. 'om' on line 44.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setmainfont with sig. 'om' on line 54.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setsansfont with sig. 'om' on line 64.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setmonofont with sig. 'om' on line 74.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setmathrm with sig. 'om' on line 88.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setboldmathrm with sig. 'om' on line 96.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setmathsf with sig. 'om' on line 104.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \setmathtt with sig. 'om' on line 112.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newfontfamily with sig. 'mom' on line 126.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newfontface with sig. 'mom' on line 141.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \defaultfontfeatures with sig. 't+om' on line 155.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \addfontfeatures with sig. 'm' on line 210.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newfontfeature with sig. 'mm' on line 221.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newAATfeature with sig. 'mmmm' on line 229.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newopentypefeature with sig. 'mmm' on line 237.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \aliasfontfeature with sig. 'mm' on line 261.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \aliasfontfeatureoption with sig. 'mmm' on line 270.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newfontscript with sig. 'mm' on line 275.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \newfontlanguage with sig. 'mm' on line 301.
.................................................
.................................................
. LaTeX info: "xparse/define-command"
. 
. Defining command \DeclareFontsExtensions with sig. 'm' on line 321.
.................................................
\l__fontspec_tmp_int=\count329
LaTeX Info: Redefining \itshape on input line 2230.
LaTeX Info: Redefining \slshape on input line 2235.
LaTeX Info: Redefining \scshape on input line 2240.
LaTeX Info: Redefining \upshape on input line 2245.

("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec.cfg")))
("C:\Program Files\MiKTeX 2.9\tex\latex\xkeyval\xkeyval.sty"
Package: xkeyval 2014/12/03 v2.7a package option processing (HA)

("C:\Program Files\MiKTeX 2.9\tex\generic\xkeyval\xkeyval.tex"
("C:\Program Files\MiKTeX 2.9\tex\generic\xkeyval\xkvutils.tex"
\XKV@toks=\toks51
\XKV@tempa@toks=\toks52
)
\XKV@depth=\count330
File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA)
))
\c@eu@=\count331
\c@eu@i=\count332
\c@mkern=\count333
)
\g__file_internal_ior=\read6
Requested font "Calibri" at 10.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
\g__fontspec_family_Calibri_int=\count334
Requested font "Calibri/BI/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibriz.ttf
Requested font "Calibri/B/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "Calibri/I/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "Calibri/B/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "Calibri/B/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "Calibri/I/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "Calibri/I/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "Calibri/BI/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibriz.ttf
Requested font "Calibri/BI/OT" at 10.0pt
 -> C:/WINDOWS/Fonts/calibriz.ttf
.................................................
. fontspec info: "defining-font"
. 
. Font family 'Calibri(0)' created for font 'Calibri' with options
. [Ligatures=TeX,Mapping=tex-text].
. 
. This font family consists of the following shapes:
. 
. * 'normal' with NFSS spec.:
. 
. <->"Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;"
. 
. * 'small caps' with NFSS spec.:
. 
. <->"Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;+s
mcp;"
. and font adjustment code:
. 
. 
. * 'bold' with NFSS spec.:
. 
. <->"Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;
"
. 
. * 'bold small caps' with NFSS spec.:
. 
. <->"Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;
+smcp;"
. and font adjustment code:
. 
. 
. * 'italic' with NFSS spec.:
. 
. <->"Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;
"
. 
. * 'small caps' with NFSS spec.:
. 
. <->"Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text;
+smcp;"
. and font adjustment code:
. 
. 
. * 'bold italic' with NFSS spec.:
. 
. <->"Calibri/BI/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text
;"
. 
. * 'bold small caps' with NFSS spec.:
. 
. <->"Calibri/BI/OT:script=latn;language=DFLT;mapping=tex-text;mapping=tex-text
;+smcp;"
. and font adjustment code:
. 
.................................................
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 10.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
\symDigits:m:n=\mathgroup7
\symLatin:m:n=\mathgroup8
\symLatin:m:it=\mathgroup9
\symGreek:m:n=\mathgroup10
\symGreek:m:it=\mathgroup11
LaTeX Font Info:    Redeclaring math alphabet \mathrm on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathrm' in version `bold'
(Font)                  EU1/Calibri(0)/m/n --> EU1/Calibri(0)/bx/n on input lin
e 48.
LaTeX Font Info:    Redeclaring math alphabet \mathit on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `normal'
(Font)                  OT1/cmr/m/it --> EU1/Calibri(0)/m/it on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
(Font)                  OT1/cmr/bx/it --> EU1/Calibri(0)/m/it on input line 48.

LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `normal'
(Font)                  OT1/cmr/bx/n --> EU1/Calibri(0)/bx/n on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `bold'
(Font)                  OT1/cmr/bx/n --> EU1/Calibri(0)/bx/n on input line 48.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
(Font)                  EU1/Calibri(0)/m/it --> EU1/Calibri(0)/bx/it on input l
ine 48.
\symOperators:m:n=\mathgroup12
Requested font "[cmmi10]" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/OT" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
.................................................
. fontspec info: "no-scripts"
. 
. Font [cmmi10] does not contain any OpenType `Script' information.
.................................................
\g__fontspec_family_[cmmi10]_int=\count335
Requested font "[cmmi10]/BI/OT" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/B/OT" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
.................................................
. fontspec info: "defining-font"
. 
. Font family '[cmmi10](0)' created for font '[cmmi10]' with options
. [Ligatures=TeX].
. 
. This font family consists of the following shapes:
. 
. * 'normal' with NFSS spec.:
. <->"[cmmi10]/OT:mapping=tex-text;"
. 
. * 'small caps' with NFSS spec.:
. 
. and font adjustment code:
. 
. 
. * 'bold' with NFSS spec.:
. <->"[cmmi10]/B/OT:mapping=tex-text;"
. 
. * 'bold small caps' with NFSS spec.:
. 
. and font adjustment code:
. 
. 
. * 'italic' with NFSS spec.:
. <->"[cmmi10]/I/OT:mapping=tex-text;"
. 
. * 'small caps' with NFSS spec.:
. 
. and font adjustment code:
. 
. 
. * 'bold italic' with NFSS spec.:
. <->"[cmmi10]/BI/OT:mapping=tex-text;"
. 
. * 'bold small caps' with NFSS spec.:
. 
. and font adjustment code:
. 
.................................................
LaTeX Font Info:    Redeclaring symbol font `Greek:m:n' on input line 48.
LaTeX Font Info:    Overwriting symbol font `Greek:m:n' in version `normal'
(Font)                  EU1/Calibri(0)/m/n --> EU1/[cmmi10](0)/m/n on input lin
e 48.
LaTeX Font Info:    Overwriting symbol font `Greek:m:n' in version `bold'
(Font)                  EU1/Calibri(0)/m/n --> EU1/[cmmi10](0)/m/n on input lin
e 48.
LaTeX Font Info:    Redeclaring symbol font `Greek:m:it' on input line 48.
LaTeX Font Info:    Overwriting symbol font `Greek:m:it' in version `normal'
(Font)                  EU1/Calibri(0)/m/it --> EU1/[cmmi10](0)/m/it on input l
ine 48.
LaTeX Font Info:    Overwriting symbol font `Greek:m:it' in version `bold'
(Font)                  EU1/Calibri(0)/m/it --> EU1/[cmmi10](0)/m/it on input l
ine 48.
Requested font "[cmmi10]/OT:mapping=tex-text;" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
\c@HW=\count336
\c@HWindent=\count337

(Math1010text.aux)
LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for PU/pdf/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for EU1/lmr/m/n on input line 66.
LaTeX Font Info:    ... okay on input line 66.
LaTeX Font Info:    Checking defaults for T3/cmr/m/n on input line 66.
LaTeX Font Info:    Try loading font information for T3+cmr on input line 66.
 ("C:\Program Files\MiKTeX 2.9\tex\latex\tipa\t3cmr.fd"
File: t3cmr.fd 2001/12/31 TIPA font definitions
)
LaTeX Font Info:    ... okay on input line 66.
\AtBeginShipoutBox=\box95

("C:\Program Files\MiKTeX 2.9\tex\latex\oberdiek\pdflscape.sty"
Package: pdflscape 2008/08/11 v0.10 Display of landscape pages in PDF (HO)

("C:\Program Files\MiKTeX 2.9\tex\latex\graphics\lscape.sty"
Package: lscape 2000/10/22 v3.01 Landscape Pages (DPC)
)
Package pdflscape Info: Auto-detected driver: dvipdfm (xetex) on input line 98.

)
*geometry* detected driver: pdftex
*geometry* verbose mode - [ preamble ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.26999pt, 320.0pt, 222.02501pt)
* v-part:(T,H,B)=(72.27pt, 650.43pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=320.0pt
* \textheight=650.43pt
* \oddsidemargin=0.0pt
* \evensidemargin=149.75502pt
* \topmargin=-30.06747pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

ABD: EveryShipout initializing macros
Package hyperref Info: Link coloring OFF on input line 66.

("C:\Program Files\MiKTeX 2.9\tex\latex\hyperref\nameref.sty"
Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section

("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\gettitlestring.sty"
Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO)
)
\c@section@level=\count338
)
LaTeX Info: Redefining \ref on input line 66.
LaTeX Info: Redefining \pageref on input line 66.
LaTeX Info: Redefining \nameref on input line 66.

(Math1010text.out) (Math1010text.out)
\@outlinefile=\write6
Package caption Info: Begin \AtBeginDocument code.
Package caption Info: End \AtBeginDocument code.

Package pgfplots notification 'compat/show suggested version=true': you might b
enefit from \pgfplotsset{compat=1.12} (current compat level: 1.8).

(text_pre/front_matter_and_coverI.tex (text_pre/title_pageI.tex
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;+smcp;" at 10.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;+smcp;" at 24.88pt
 -> C:/WINDOWS/Fonts/calibri.ttf
LaTeX Font Info:    Font shape `EU1/Calibri(0)/m/sl' in size <10> not available

(Font)              Font shape `EU1/Calibri(0)/m/it' tried instead on input lin
e 11.
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
LaTeX Font Info:    Font shape `EU1/Calibri(0)/m/sl' in size <14.4> not availab
le
(Font)              Font shape `EU1/Calibri(0)/m/it' tried instead on input lin
e 11.
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 14.4pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 14.4pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 14.4pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 12.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "cmr12" at 14.4pt
Requested font "cmmi12" at 14.4pt
Requested font "cmsy10" at 14.4pt
Requested font "cmex10" at 14.4pt
Requested font "cmex7" at 7.0pt
LaTeX Font Info:    Try loading font information for U+msa on input line 27.

("C:\Program Files\MiKTeX 2.9\tex\latex\amsfonts\umsa.fd"
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
)
Requested font "msam10" at 14.4pt
Requested font "msam10" at 10.0pt
Requested font "msam7" at 7.0pt
LaTeX Font Info:    Try loading font information for U+msb on input line 27.

("C:\Program Files\MiKTeX 2.9\tex\latex\amsfonts\umsb.fd"
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
)
Requested font "msbm10" at 14.4pt
Requested font "msbm10" at 10.0pt
Requested font "msbm7" at 7.0pt
LaTeX Font Info:    Try loading font information for U+esvect on input line 27.


("C:\Program Files\MiKTeX 2.9\tex\latex\esvect\uesvect.fd"
File: uesvect.fd 
)
Requested font "vect10" at 14.4pt
Requested font "vect10" at 10.0pt
Requested font "vect7" at 7.0pt
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 7.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 7.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "[cmmi10]/OT:mapping=tex-text;" at 14.4pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/OT:mapping=tex-text;" at 7.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 14.4pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 7.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "cmex7" at 5.0pt
Requested font "msam5" at 5.0pt
Requested font "msbm5" at 5.0pt
Requested font "vect5" at 5.0pt
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 5.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 5.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "[cmmi10]/OT:mapping=tex-text;" at 5.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 5.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb

Overfull \hbox (140.0pt too wide) in paragraph at lines 3--47
[] $[]$ 
 []

) ("C:\Program Files\MiKTeX 2.9\tex\generic\oberdiek\se-ascii-print.def"
File: se-ascii-print.def 2011/12/02 v1.10 stringenc: Printable ASCII characters

)
[1


] (text_pre/copyright_pageI.tex
File: figures/license.pdf Graphic file (type QTm)
 <use  "figures/license.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 10--11
[]\EU1/Calibri(0)/m/n/10 Licensed under the Creative Commons Attribution-
 []


Overfull \hbox (6.72217pt too wide) in paragraph at lines 2--12
 $[]$ $[]$ 
 []

File: text/by-nc.pdf Graphic file (type QTm)
<use  "text/by-nc.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 28--29
[]\EU1/Calibri(0)/m/n/10 Licensed under the Creative Commons Attribution-
 []


Overfull \hbox (6.72217pt too wide) in paragraph at lines 20--30
 $[]$ $[]$ 
 []

File: figures/license.pdf Graphic file (type QTm)
<use  "figures/license.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 45--46
[]\EU1/Calibri(0)/m/n/10 This work is licensed under the Creative Commons
 []


Underfull \hbox (badness 10000) in paragraph at lines 45--46
\EU1/Calibri(0)/m/n/10 Attribution-Noncommercial-ShareAlike 4.0 International
 []

)
Overfull \hbox (6.72217pt too wide) in paragraph at lines 37--48
 $[]$ $[]$
 []

[2

]
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 24.88pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 24.88pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
 (Math1010text.toc
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 10.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
 [3


] [4])
\tf@toc=\write7
 [5] [6


]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.26999pt, 320.0pt, 222.02501pt)
* v-part:(T,H,B)=(72.27pt, 650.43pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=320.0pt
* \textheight=650.43pt
* \oddsidemargin=0.0pt
* \evensidemargin=149.75502pt
* \topmargin=-30.06747pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=108.405pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 (text_pre/prefaceI.tex
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;+smcp;" at 24.88pt
 -> C:/WINDOWS/Fonts/calibrib.ttf

Underfull \hbox (badness 10000) in paragraph at lines 3--5

 []

[7

]
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 12.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf

Underfull \hbox (badness 10000) in paragraph at lines 20--21

 []

) [8])
Chapter 1.
(text_pre/00_SetTheory.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 15--16
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 15--16

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 35--37
[][][]
 []


Overfull \hbox (7.03586pt too wide) in paragraph at lines 38--38
\EU1/Calibri(0)/m/n/10 “pronghorns.” Also, the \EU1/Calibri(0)/m/it/10 order \E
U1/Calibri(0)/m/n/10 of the elements doesn’t matter, so $[]$
 []


Overfull \hbox (43.60371pt too wide) in paragraph at lines 41--43
\EU1/Calibri(0)/m/n/10 sign ‘$\OT1/cmr/m/n/10 =$\EU1/Calibri(0)/m/n/10 ’ and wr
ite $[] \OT1/cmr/m/n/10 = []$ \EU1/Calibri(0)/m/n/10 or $[] \OT1/cmr/m/n/10 = \
OMS/cmsy/m/n/10 f[] j []g$\EU1/Calibri(0)/m/n/10 .
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 57--58
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 57--58

 []


Underfull \vbox (badness 5008) has occurred while \output is active []

Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
 [1







]
Overfull \hbox (10.94987pt too wide) in paragraph at lines 61--62
[]\EU1/Calibri(0)/m/n/10 Now let’s consider the set $[] \OT1/cmr/m/n/10 = \OMS/
cmsy/m/n/10 f[] j []g$\EU1/Calibri(0)/m/n/10 .
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 67--68
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 67--68

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 85--86
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []

[2]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 99--100
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 99--100

 []

Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 12.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf

Overfull \hbox (1.39998pt too wide) in paragraph at lines 142--143
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 142--143

 []

File: figures/RelationsandFunctionsGraphics/SetTheory-1.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/SetTheory-1.pdf" >
Requested font "cmr9" at 9.0pt
Requested font "cmr6" at 6.0pt
Requested font "cmmi9" at 9.0pt
Requested font "cmmi6" at 6.0pt
Requested font "cmsy9" at 9.0pt
Requested font "cmsy6" at 6.0pt
Requested font "cmex9" at 9.0pt
Requested font "cmex7" at 6.0pt
Requested font "msam10" at 9.0pt
Requested font "msam7" at 6.0pt
Requested font "msbm10" at 9.0pt
Requested font "msbm7" at 6.0pt
Requested font "vect9" at 9.0pt
Requested font "vect6" at 6.0pt
Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 6.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 6.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "[cmmi10]/OT:mapping=tex-text;" at 9.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/OT:mapping=tex-text;" at 6.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 9.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 6.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
File: figures/RelationsandFunctionsGraphics/SetTheory-2.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/SetTheory-2.pdf" >
File: figures/RelationsandFunctionsGraphics/SetTheory-3.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/SetTheory-3.pdf" >
File: figures/RelationsandFunctionsGraphics/SetTheory-4.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/SetTheory-4.pdf" > [3]
Overfull \hbox (0.88911pt too wide) detected at line 177
\U/msb/m/n/10 Q \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f[] j []g
 []


Overfull \hbox (51.99902pt too wide) in paragraph at lines 153--181
 $[]$ 
 []


Underfull \hbox (badness 10000) in paragraph at lines 238--238

 []

Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;+smcp;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;+smcp;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf

Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 An example of a number with a
 []


Underfull \hbox (badness 10000) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 repeating decimal expansion is
 []


Underfull \hbox (badness 1297) has occurred while \output is active
[] \OT1/cmr/m/n/9 = []\OML/cmm/m/it/9 :[][][][][][][][][][][] []$\EU1/Calibri(0
)/m/n/9 . This is ra-
 []


Underfull \hbox (badness 5446) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 This gives us the rational expression
 []


Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The classic example of an irrational
 []


Underfull \hbox (badness 7291) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 number is the number $[]$ (See Sec-
 []


Underfull \hbox (badness 5147) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 tion []8.1[]), but numbers like $[]$ and
 []


Underfull \hbox (badness 3646) has occurred while \output is active
[]\OML/cmm/m/it/9 :[][][][][][][][][][][][][][][] []$ \EU1/Calibri(0)/m/n/9 are
 other fine
 []

[4] [5]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 257--258
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 257--258

 []


Overfull \hbox (11.52426pt too wide) detected at line 276
[]
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 276--278
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 276--278

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-1.pdf Graphic file (
type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-1.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-2.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-2.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-3.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-3.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-4.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-4.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-5.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-5.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-6.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-6.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-7.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-7.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-8.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-8.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-9.pdf Graphic file (
type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-9.pdf" >
Overfull \hbox (9.6117pt too wide) in paragraph at lines 356--356
 [] 
 []


Overfull \hbox (32.00195pt too wide) in paragraph at lines 285--360
$[]$ 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/RelationsandFunctionsGraphics/SetTheory-5.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/SetTheory-5.pdf" > [6]
File: figures/RelationsandFunctionsGraphics/CartesianPlane-10.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-10.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-11.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-11.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-12.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-12.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-13.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-13.pdf" > [7]
File: figures/RelationsandFunctionsGraphics/CartesianPlane-14.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-14.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-15.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-15.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-16.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-16.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-17.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-17.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-18.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-18.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-19.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-19.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-20.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-20.pdf" > [8]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 20.74pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 20.74pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
File: figures/RelationsandFunctionsGraphics/CartesianPlane-32.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-32.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-33.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-33.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-34.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-34.pdf" >
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
 [9

])
(text_pre/00_RealNumberArithmetic.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 26--27
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 26--27

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 50--51
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 50--51

 []

[10

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 69--70
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 69--70

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 104--105
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 104--105

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [11]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 152--153
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 152--153

 []


Underfull \hbox (badness 1286) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The expression $[]$ is technically an ‘in-
 []


Underfull \hbox (badness 2828) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 determinate form’ as opposed to be-
 []


Underfull \hbox (badness 2181) has occurred while \output is active
[]\EU1/Calibri(0)/bx/n/9 Note: \EU1/Calibri(0)/m/n/9 A common denominator \EU1/
Calibri(0)/bx/n/9 is \EU1/Calibri(0)/m/n/9 re-
 []


Underfull \hbox (badness 2189) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 mon factors - this is really just read-
 []

[12]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 181--182
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 181--182

 []


Overfull \hbox (7.54182pt too wide) in paragraph at lines 332--332
[]$[]$ 
 []


Overfull \hbox (21.28006pt too wide) in paragraph at lines 332--332
[]$[]$[] 
 []


Underfull \hbox (badness 2790) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 It might be junior high (elementary?)
 []


Underfull \hbox (badness 3179) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 tions, we strongly recommend seeing
 []


Underfull \hbox (badness 2753) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 (and even formal educational []$[]$[])
 []

[13]
Overfull \hbox (25.00003pt too wide) in paragraph at lines 332--332
[]$[]$ 
 []

[14]
Overfull \hbox (25.00003pt too wide) in paragraph at lines 332--332
[]$[]$ 
 []


Overfull \hbox (18.67111pt too wide) detected at line 332
[] \OT1/cmr/m/n/10 = []
 []

[15] [16]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 368--369
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 368--369

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 389--390
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 389--390

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [17]
Underfull \hbox (badness 10000) in paragraph at lines 479--479
[]$[][]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 )(\OMS/cmsy/m/n/1
0 ^^@[] \OT1/cmr/m/n/10 + [])[] +
 []


Underfull \hbox (badness 1490) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Order of operations follows the “PED-
 []

[18] [19]
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 7.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 5.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
Requested font "cmbx10" at 10.0pt
Requested font "cmbx7" at 7.0pt
Requested font "cmbx5" at 5.0pt
Requested font "cmmib10" at 10.0pt
Requested font "cmmib7" at 7.0pt
Requested font "cmmib5" at 5.0pt
Requested font "cmbsy10" at 10.0pt
Requested font "cmbsy7" at 7.0pt
Requested font "cmbsy5" at 5.0pt

Overfull \hbox (1.39998pt too wide) in paragraph at lines 490--491
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 490--491

 []


Overfull \hbox (18.10443pt too wide) in paragraph at lines 495--496
[]\EU1/Calibri(0)/m/n/10 15[] can be found in the Properties of Negatives. Firs
t, for all real numbers, $[][] \OMS/cmsy/m/n/10 ^^U
 []

[20]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 523--524
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 523--524

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 554--555
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 554--555

 []


Underfull \hbox (badness 2088) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 (disappointingly?), that’s not a can of
 []

[21]
Underfull \vbox (badness 10000) has occurred while \output is active []

 [22]
Overfull \hbox (0.8197pt too wide) in paragraph at lines 646--646
\EU1/Calibri(0)/m/n/10 isn’t a perfect cube, (of an integer, that is!) we may t
hink of $\OMS/cmsy/m/n/10 ^^@[] \OT1/cmr/m/n/10 = (\OMS/cmsy/m/n/10 ^^@[]\OT1/c
mr/m/n/10 )([])$\EU1/Calibri(0)/m/n/10 .
 []

[23]
Overfull \hbox (6.91644pt too wide) in paragraph at lines 646--646
\EU1/Calibri(0)/m/n/10 out that these fractions reduce even further. Since $[] 
\OT1/cmr/m/n/10 = [][]$\EU1/Calibri(0)/m/n/10 , $[][] \OT1/cmr/m/n/10 = ([][])[
] =
 []

[24] [25]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [26

]) (text_pre/01_CartesianPlane.tex
File: figures/RelationsandFunctionsGraphics/CartesianPlane-21.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-21.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-22.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-22.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-23.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-23.pdf" >
Overfull \hbox (11.99802pt too wide) in paragraph at lines 33--39
[][] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [27

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 62--63
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 62--63

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-24.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-24.pdf" >
Overfull \hbox (1.9992pt too wide) in paragraph at lines 77--77
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [28]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 112--113
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 112--113

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-25.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-25.pdf" >
Overfull \hbox (25.79848pt too wide) has occurred while \output is active
 [][] 
 []

[29]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 186--187
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 186--187

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-26.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-26.pdf" >
Overfull \hbox (23.9996pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-27.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-27.pdf" >
Overfull \hbox (13.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[30]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 217--218
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 217--218

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-28.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-28.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-29.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-29.pdf" >
Overfull \hbox (6.99963pt too wide) has occurred while \output is active
 [][] 
 []

[31]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 291--292
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 291--292

 []

File: figures/RelationsandFunctionsGraphics/CartesianPlane-30.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-30.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-31.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-31.pdf" > [32]
[33]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/RelationsandFunctionsGraphics/CartesianPlane-35.pdf Graphic file 
(type QTm)
 <use  "figures/RelationsandFunctionsGraphics/CartesianPlane-35.pdf" >
[34

]) (text_pre/00_CmpNums.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 20--21
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 20--21

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 34--35
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 34--35

 []


Underfull \vbox (badness 3386) has occurred while \output is active []


Underfull \hbox (badness 1603) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 label the imaginary unit ‘$[]$’, usually to
 []

[35

]
Overfull \hbox (4.87463pt too wide) in paragraph at lines 118--118
\EU1/Calibri(0)/m/n/10 plicable to real numbers to get $[][] \OT1/cmr/m/n/10 = 
[] [] = [][][] =
 []

[36]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 143--144
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 143--144

 []

[37]
Underfull \hbox (badness 1655) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 it would be unfair to tackle quadratic
 []

[38]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 254--255
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 254--255

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [39]
[40]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [41

]) [42



]
Chapter 2.
(text_pre/01_Relations.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 11--12
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 11--12

 []


Overfull \hbox (22.44398pt too wide) in paragraph at lines 91--91
[]$[] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ;
 []\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@[]\
OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 ([]\OML
/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 (\OMS/cmsy
/m/n/10 ^^@[]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 g$ 
 []


Overfull \hbox (4.02005pt too wide) in paragraph at lines 91--91
[]$[] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ;
 []\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 j []g$ 
 []

File: figures/RelationsandFunctionsGraphics/Relations-1.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/Relations-1.pdf" >
Overfull \hbox (3.6002pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/Relations-2.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/Relations-2.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-3.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-3.pdf" > [43

]
File: figures/RelationsandFunctionsGraphics/Relations-8.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-8.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 91--91
$[]$ 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 108--109
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 108--109

 []

File: figures/RelationsandFunctionsGraphics/Relations-4.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/Relations-4.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-5.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-5.pdf" >
Overfull \hbox (7.60019pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/RelationsandFunctionsGraphics/Relations-6.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/Relations-6.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-7.pdf Graphic file (type 
QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-7.pdf" > [44]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 126--127
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 126--127

 []

[45]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 223--224
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 223--224

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 242--243
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 242--243

 []

File: figures/RelationsandFunctionsGraphics/Relations-9.pdf Graphic file (type 
QTm)
<use  "figures/RelationsandFunctionsGraphics/Relations-9.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-10.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-10.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][] 
 []

[46]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 269--270
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 269--270

 []

[47]
File: figures/RelationsandFunctionsGraphics/Relations-11.pdf Graphic file (type
 QTm)
 <use  "figures/RelationsandFunctionsGraphics/Relations-11.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-12.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-12.pdf" > [48] [49]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/RelationsandFunctionsGraphics/Relations-14.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-14.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-15.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-15.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-16.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-16.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-17.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-17.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-18.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-18.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-19.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-19.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-20.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-20.pdf" > [50

]
File: figures/RelationsandFunctionsGraphics/Relations-21.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-21.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-22.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-22.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-22.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-22.pdf" >
Overfull \hbox (16.53235pt too wide) in paragraph at lines 346--346
[]$\OMS/cmsy/m/n/9 f[] \OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\
OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/
m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9
 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \O
T1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/
m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (
[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/
cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; []\OMS/cmsy/m/n/9 g$ 
 []

[51] [52]) (text_pre/01_IntrotoFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 10--11
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 10--11

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 52--53
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 52--53

 []


Underfull \vbox (badness 4699) has occurred while \output is active []

File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-1.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-1.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-2.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-2.pdf" > [53

]
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-3.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-3.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-4.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-4.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-5.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-5.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-6.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-6.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-7.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-7.pdf" > [54]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 119--121
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 119--121

 []

File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-8.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-8.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-9.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-9.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-10.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-10.pdf" >
[55]
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-11.pdf Graphic fil
e (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-11.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-12.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-12.pdf" >
[56]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


Overfull \hbox (16.53235pt too wide) in paragraph at lines 228--228
[]$\OMS/cmsy/m/n/9 f[] \OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\
OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/
m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9
 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \O
T1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/
m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (
[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/
cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; []\OMS/cmsy/m/n/9 g$ 
 []

File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-13.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-13.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-14.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-14.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-15.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-15.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-16.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-16.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-17.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-17.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-18.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-18.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-19.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-19.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-20.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-20.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-21.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-21.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-22.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-22.pdf" >
[57

]
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-23.pdf Graphic fil
e (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-23.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-24.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-24.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-25.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-25.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-26.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-26.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-27.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-27.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-28.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-28.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-29.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-29.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-30.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-30.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-31.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-31.pdf" >
File: figures/RelationsandFunctionsGraphics/IntrotoFunctions-32.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/IntrotoFunctions-32.pdf" >
[58]
Overfull \hbox (16.53235pt too wide) in paragraph at lines 228--228
[]$\OMS/cmsy/m/n/9 f[] \OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\
OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (\OMS/cmsy/
m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9
 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \O
T1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/
m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 (
[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/
cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; []\OMS/cmsy/m/n/9 g$ 
 []

[59]) (text_pre/01_FunctionNotation.tex
File: figures/RelationsandFunctionsGraphics/FunctionNotation-1.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/FunctionNotation-1.pdf" >
Overfull \hbox (22.49957pt too wide) has occurred while \output is active
 [][][] 
 []

[60

] [61] [62] [63] [64] [65]
Overfull \hbox (0.22742pt too wide) in paragraph at lines 263--264
[]\EU1/Calibri(0)/m/n/10 Mathematical modelling is not a one-section topic. It’
s not even a one-\EU1/Calibri(0)/m/it/10 course
 []

[66]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [67

] [68]
Requested font "cmbx9" at 9.0pt
Requested font "cmbx6" at 6.0pt
Requested font "cmmib9" at 9.0pt
Requested font "cmmib6" at 6.0pt
Requested font "cmbsy9" at 9.0pt
Requested font "cmbsy6" at 6.0pt
 [69]) (text_pre/01_FunctionArithmetic.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 24--25
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 24--25

 []

[70

]
Overfull \hbox (14.14743pt too wide) in paragraph at lines 108--108
[]\EU1/Calibri(0)/m/n/10 Alternatively, we may proceed as above and analyze the
 expression $[] \OT1/cmr/m/n/10 ([]) =
 []

[71]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 124--125
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 124--125

 []

[72]
Underfull \vbox (badness 5832) has occurred while \output is active []

 [73]
Overfull \hbox (15.00003pt too wide) in paragraph at lines 212--212
 $[]$ 
 []

[74]
Overfull \hbox (1.14368pt too wide) in paragraph at lines 218--219
[]\EU1/Calibri(0)/m/n/10 As mentioned before, we will revisit difference quotie
nts in Section []3.1[] where
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 242--243
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 242--243

 []

[75] [76] [77]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [78

]
Overfull \hbox (14.46515pt too wide) detected at line 286
[] \OT1/cmr/m/n/9 = \OMS/cmsy/m/n/9 f\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/
cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^@[]\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/
n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ;
 \OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^@[]\O
T1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/
m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^
@[]\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1
/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/
n/9 )\OMS/cmsy/m/n/9 g\OML/cmm/m/it/9 :
 []

[79]) (text_pre/01_GraphsofFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 12--13
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 12--13

 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-1.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-1.pdf" >
[80

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 94--95
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 94--95

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 114--115
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 114--115

 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-2.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-2.pdf" >
Underfull \hbox (badness 1400) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Note that for graphs of functions, we
 []

[81]
Underfull \hbox (badness 5008) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 A good resource when you need to
 []


Underfull \hbox (badness 1253) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 you can run locally on a computer or
 []

File: figures/RelationsandFunctionsGraphics/GoF-1.png Graphic file (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GoF-1.png" >
Overfull \hbox (0.99963pt too wide) has occurred while \output is active
 [][][] 
 []

[82]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_02.png Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_02.png" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_03.png Graphic fi
le (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_03.png" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_04.png Graphic fi
le (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_04.png" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[83]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_05.png Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_05.png" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_06.png Graphic fi
le (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_06.png" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[84]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 282--283
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 282--283

 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-3.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-3.pdf" >
Overfull \hbox (21.20021pt too wide) has occurred while \output is active
 [][] 
 []


Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Typically, in (pre)calculus, whenever
 []

[85]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 322--323
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 322--323

 []

[86]
Overfull \hbox (2.08667pt too wide) in paragraph at lines 402--402
\EU1/Calibri(0)/m/n/10 sponds to a point on the graph is everything from $\OMS/
cmsy/m/n/10 ^^@[]$ \EU1/Calibri(0)/m/n/10 to $[]$, inclusive. Hence,
 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-4.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-4.pdf" >
Overfull \hbox (23.6002pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-5.pdf Graphic fil
e (type QTm)
<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-5.pdf" >
[87]
LaTeX Font Info:    Try loading font information for EU1+lmtt on input line 419
.
 ("C:\Program Files\MiKTeX 2.9\tex\latex\euenc\eu1lmtt.fd"
File: eu1lmtt.fd 2009/10/30 v1.6 Font defs for Latin Modern
)
Requested font "[lmmono10-regular]" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmmono10-regular.otf
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_07.png Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_07.png" >
Overfull \hbox (2.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[88]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions_08.png Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions_08.png" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []


Underfull \hbox (badness 1215) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 It seems silly to list a final answer as
 []

[89]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-6.pdf Graphic fil
e (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-6.pdf" >
[90

]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-7.pdf Graphic fil
e (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-7.pdf" >
[91]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-8.pdf Graphic fil
e (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-8.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-9.pdf Graphic fil
e (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-9.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-10.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-10.pdf" >
[92]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-11.pdf Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-11.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-12.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-12.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-13.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-13.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-14.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-14.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-15.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-15.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-16.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-16.pdf" >
[93]) (text_pre/01_Transformations.tex
File: figures/RelationsandFunctionsGraphics/Transformations-2.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-2.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-3.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-3.pdf" >
Overfull \hbox (50.64285pt too wide) in paragraph at lines 32--41
 [][] 
 []

File: figures/RelationsandFunctionsGraphics/Transformations-1.pdf Graphic file 
(type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-1.pdf" > [94

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 60--61
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 60--61

 []

[95]
File: figures/RelationsandFunctionsGraphics/Transformations-4.pdf Graphic file 
(type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations-4.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-5.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-5.pdf" >
Overfull \hbox (28.52615pt too wide) in paragraph at lines 102--111
 [][] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 130--131
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 130--131

 []


Underfull \hbox (badness 10000) in paragraph at lines 196--196

 []

[96]
File: figures/RelationsandFunctionsGraphics/Transformations-6.pdf Graphic file 
(type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations-6.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-8.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-8.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-10.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-10.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-12.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-12.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-14.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-14.pdf" > [97]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 214--215
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 214--215

 []

File: figures/RelationsandFunctionsGraphics/Transformations-15.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-15.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-16.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-16.pdf" >
Overfull \hbox (61.80804pt too wide) in paragraph at lines 226--235
 [][] 
 []

File: figures/RelationsandFunctionsGraphics/Transformations-17.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-17.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-18.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-18.pdf" >
Overfull \hbox (153.7087pt too wide) in paragraph at lines 246--255
 [][] 
 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 243--257
 $[]$ 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 1286) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 was even, odd or neither. The inter-
 []

[98]
File: figures/RelationsandFunctionsGraphics/Transformations-19.pdf Graphic file
 (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations-19.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-20.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-20.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-22.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-22.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-24.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-24.pdf" > [99]
File: figures/RelationsandFunctionsGraphics/Transformations-26.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-26.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-28.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-28.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-29.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-29.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-31.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-31.pdf" > [100]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 359--360
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 359--360

 []

File: figures/RelationsandFunctionsGraphics/Transformations-33.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-33.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-34.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-34.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-35.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-35.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-37.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-37.pdf" >
Overfull \hbox (14.99962pt too wide) has occurred while \output is active
 [][] 
 []

[101]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 436--437
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 436--437

 []

File: figures/RelationsandFunctionsGraphics/Transformations-40.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-40.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-39.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-39.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-41.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-41.pdf" > [102]
Overfull \hbox (23.56723pt too wide) in paragraph at lines 494--494
[]\EU1/Calibri(0)/m/n/10 We now examine what’s happening to the outputs. From $
[]\OT1/cmr/m/n/10 ([]) = \OMS/cmsy/m/n/10 ^^@[] [] \OT1/cmr/m/n/10 +
 []

File: figures/RelationsandFunctionsGraphics/Transformations-43.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-43.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/Transformations-45.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-45.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/Transformations-47.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-47.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/RelationsandFunctionsGraphics/Transformations-49.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-49.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[103]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 516--517
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 516--517

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [104]
Overfull \hbox (4.6664pt too wide) in paragraph at lines 577--577
[]\EU1/Calibri(0)/m/n/10 Next, we take each of the $[]$ values and substitute t
hem into $[]\OT1/cmr/m/n/10 ([]) = \OMS/cmsy/m/n/10 ^^@[][]\OT1/cmr/m/n/10 (\OM
S/cmsy/m/n/10 ^^@[][] \OT1/cmr/m/n/10 +
 []


Overfull \hbox (10.52744pt too wide) detected at line 577
[] [] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@[][] [] \OT1/cmr/m/n/10 + [] = \OMS
/cmsy/m/n/10 ^^@[][]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 ) + 
[] = \OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/
10 ) + [] = [] + [] = []
 []

File: figures/RelationsandFunctionsGraphics/Transformations-51.pdf Graphic file
 (type QTm)
<use  "figures/RelationsandFunctionsGraphics/Transformations-51.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-52.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-52.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-50.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-50.pdf" >
Overfull \hbox (11.6002pt too wide) has occurred while \output is active
 [][][] 
 []


Overfull \hbox (9.29395pt too wide) has occurred while \output is active
 [][] 
 []

[105]
File: figures/RelationsandFunctionsGraphics/Transformations01.png Graphic file 
(type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations01.png" >
File: figures/RelationsandFunctionsGraphics/Transformations02.png Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations02.png" >
File: figures/RelationsandFunctionsGraphics/Transformations03.png Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations03.png" >
File: figures/RelationsandFunctionsGraphics/Transformations04.png Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations04.png" >
File: figures/RelationsandFunctionsGraphics/Transformations05.png Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations05.png" >
Overfull \hbox (7.67908pt too wide) has occurred while \output is active
 [][] 
 []

[106]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/RelationsandFunctionsGraphics/Transformations-53.pdf Graphic file
 (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations-53.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-54.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-54.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-55.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-55.pdf" > [107

]
File: figures/RelationsandFunctionsGraphics/Transformations-56.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-56.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-57.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-57.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-58.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-58.pdf" >
Overfull \hbox (13.68547pt too wide) in paragraph at lines 631--631
[][] 
 []

[108] [109]) [110



]
Chapter 3.
(text_pre/02_LinearFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 19--20
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 19--20

 []

File: figures/LinearQuadraticGraphics/LinearFunctions-2.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-2.pdf" >
Overfull \hbox (90.35pt too wide) in paragraph at lines 105--105
[][] 
 []

File: figures/LinearQuadraticGraphics/LinearFunctions-3.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-3.pdf" >
Overfull \hbox (90.35pt too wide) in paragraph at lines 105--105
[][] 
 []

File: figures/LinearQuadraticGraphics/LinearFunctions-1.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-1.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 See []$[]$[] or
 []


Underfull \hbox (badness 10000) has occurred while \output is active
[]$[]$[] \EU1/Calibri(0)/m/n/9 for
 []

[111

]
File: figures/LinearQuadraticGraphics/LinearFunctions-4.pdf Graphic file (type 
QTm)
 <use  "figures/LinearQuadraticGraphics/LinearFunctions-4.pdf" >
Overfull \hbox (90.35pt too wide) in paragraph at lines 105--105
[][] 
 []

File: figures/LinearQuadraticGraphics/LinearFunctions-5.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-5.pdf" >
Overfull \hbox (90.35pt too wide) in paragraph at lines 105--105
[][] 
 []

File: figures/LinearQuadraticGraphics/LinearFunctions-6.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-6.pdf" >
Overfull \hbox (90.35002pt too wide) in paragraph at lines 105--105
[][] 
 []

File: figures/LinearQuadraticGraphics/LinearFunctions-7.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-7.pdf" >
Overfull \hbox (90.35002pt too wide) in paragraph at lines 105--105
[][] 
 []

[112]
File: figures/LinearQuadraticGraphics/LinearFunctions-8.pdf Graphic file (type 
QTm)
 <use  "figures/LinearQuadraticGraphics/LinearFunctions-8.pdf" > [113]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 173--174
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 173--174

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 203--204
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 203--204

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 213--214
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 213--214

 []

File: figures/LinearQuadraticGraphics/LinearFunctions-9.pdf Graphic file (type 
QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-9.pdf" > [114]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 223--224
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 223--224

 []

File: figures/LinearQuadraticGraphics/LinearFunctions-10.pdf Graphic file (type
 QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-10.pdf" >
File: figures/LinearQuadraticGraphics/LinearFunctions-11.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-11.pdf" > [115]
File: figures/LinearQuadraticGraphics/LinearFunctions-12.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-12.pdf" >
File: figures/LinearQuadraticGraphics/LinearFunctions-13.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-13.pdf" > [116]
Overfull \hbox (0.30496pt too wide) in paragraph at lines 320--320
[]\EU1/Calibri(0)/m/n/10 To find how many PortaBoys can be produced for $\OT1/c
mr/m/n/10 $[][]\OML/cmm/m/it/10 ;  [][][]$\EU1/Calibri(0)/m/n/10 , we solve $[]
\OT1/cmr/m/n/10 ([]) =
 []

[117]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 373--374
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 373--374

 []


Underfull \vbox (badness 1406) has occurred while \output is active []

 [118]
File: figures/LinearQuadraticGraphics/LinearFunctions-14.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-14.pdf" > [119] [120]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


[121

]
File: figures/LinearQuadraticGraphics/LinearFunctions-15.pdf Graphic file (type
 QTm)
 <use  "figures/LinearQuadraticGraphics/LinearFunctions-15.pdf" >
Overfull \hbox (8.0877pt too wide) in paragraph at lines 441--441
 [] 
 []

[122]
File: figures/LinearQuadraticGraphics/LinearFunctions-16.pdf Graphic file (type
 QTm)
 <use  "figures/LinearQuadraticGraphics/LinearFunctions-16.pdf" > [123])
(text_pre/02_AbsoluteValueFunctions.tex
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-1.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-1.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 24--25
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 24--25

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 56--57
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 56--57

 []

[124

] [125]
Underfull \vbox (badness 2103) has occurred while \output is active []

 [126]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-2.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-2.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-3.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-3.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-4.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-4.pdf" >
Underfull \hbox (badness 1681) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 3.9: |Constructing the graph of
 []

[127]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-5.pdf Graphic file
 (type QTm)
 <use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-5.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-6.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-6.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-7.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-7.pdf" > [128]
Underfull \vbox (badness 1895) has occurred while \output is active []

File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-8.pdf Graphic file
 (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-8.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-10.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-10.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-12.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-12.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-14.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-14.pdf" >
[129]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-15.pdf Graphic fil
e (type QTm)
 <use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-15.pdf" >
[130]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-16.pdf Graphic fil
e (type QTm)
 <use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-16.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[131]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-17.pdf Graphic fil
e (type QTm)
 <use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-17.pdf" >
[132

]) (text_pre/02_QuadraticFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 10--11
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 10--11

 []

File: figures/LinearQuadraticGraphics/QuadraticFunctions-1.pdf Graphic file (ty
pe QTm)
<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-1.pdf" >
Underfull \hbox (badness 3536) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 3.19: |The graph of the basic
 []

File: figures/LinearQuadraticGraphics/QuadraticFunctions-2.pdf Graphic file (ty
pe QTm)
<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-2.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-3.pdf Graphic file (ty
pe QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-3.pdf" > [133

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 75--76
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 75--76

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 85--86
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []

File: figures/LinearQuadraticGraphics/QuadraticFunctions-5.pdf Graphic file (ty
pe QTm)
<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-5.pdf" > [134]
Overfull \hbox (3.11539pt too wide) in paragraph at lines 102--103
\EU1/Calibri(0)/m/n/10 paragraphs have also shown us the role of the number $[]
$ in the graphs of quadratic
 []

File: figures/LinearQuadraticGraphics/QuadraticFunctions-6.pdf Graphic file (ty
pe QTm)
<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-6.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-7.pdf Graphic file (ty
pe QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-7.pdf" > [135]
File: figures/LinearQuadraticGraphics/QuadraticFunctions-8.pdf Graphic file (ty
pe QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-8.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-9.pdf Graphic file (ty
pe QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-9.pdf" > [136]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 190--191
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 190--191

 []


Overfull \hbox (0.47049pt too wide) in paragraph at lines 194--195
[]\EU1/Calibri(0)/m/n/10 There are two more results which can be gleaned from t
he completed-square
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 205--206
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 205--206

 []

[137]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 236--237
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 236--237

 []

[138]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 256--257
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 256--257

 []


Overfull \hbox (14.51698pt too wide) detected at line 305
[]\OT1/cmr/m/n/10 ([]) = []([]) \OMS/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 ([]) = [
] \OMS/cmsy/m/n/10 ^^@ [] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@[]\OML/cmm/m/it
/10 :[][][] \OT1/cmr/m/n/10 + [][][][] \OMS/cmsy/m/n/10 ^^@ [][][]\OML/cmm/m/it
/10 :
 []

[139]
File: figures/LinearQuadraticGraphics/QuadraticFunctions-10.pdf Graphic file (t
ype QTm)
 <use  "figures/LinearQuadraticGraphics/QuadraticFunctions-10.pdf" >
Overfull \hbox (9.11987pt too wide) has occurred while \output is active
 [][][] 
 []

[140]
Overfull \hbox (1.88101pt too wide) in paragraph at lines 327--327
\EU1/Calibri(0)/m/n/10 Much to Donnie’s surprise and delight, he inherits a lar
ge parcel of land in Ashtab-
 []

File: figures/LinearQuadraticGraphics/QuadraticFunctions-11.pdf Graphic file (t
ype QTm)
<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-11.pdf" > [141]
File: figures/LinearQuadraticGraphics/QuadraticFunctions-12.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-12.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-13.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-13.pdf" >
Underfull \hbox (badness 4518) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 3.28: |Obtaining the graph of
 []

[142]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

Requested font "Calibri/OT:script=latn;language=DFLT;mapping=tex-text;mapping=t
ex-text;" at 8.0pt
 -> C:/WINDOWS/Fonts/calibri.ttf
Requested font "cmr8" at 8.0pt
Requested font "cmmi8" at 8.0pt
Requested font "cmsy8" at 8.0pt
Requested font "cmex8" at 8.0pt
Requested font "msam10" at 8.0pt
Requested font "msbm10" at 8.0pt
Requested font "vect8" at 8.0pt
Requested font "Calibri/I/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 8.0pt
 -> C:/WINDOWS/Fonts/calibrii.ttf
Requested font "[cmmi10]/OT:mapping=tex-text;" at 8.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 8.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
 [143

]
Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 8.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
 [144]) (text_pre/02_Inequalities.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 67--68
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 67--68

 []

File: figures/LinearQuadraticGraphics/Inequalities-1.pdf Graphic file (type QTm
)
<use  "figures/LinearQuadraticGraphics/Inequalities-1.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-2.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-2.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-3.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-3.pdf" >
Overfull \hbox (13.73547pt too wide) has occurred while \output is active
 [][] 
 []

[145

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 131--132
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 131--132

 []


Underfull \vbox (badness 3209) has occurred while \output is active []

File: figures/LinearQuadraticGraphics/Inequalities-4.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-4.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-5.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-5.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-6.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-6.pdf" > [146]
File: figures/LinearQuadraticGraphics/Inequalities-7.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-7.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-8.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-8.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-9.pdf Graphic file (type QTm
)

<use  "figures/LinearQuadraticGraphics/Inequalities-9.pdf" > [147]
File: figures/LinearQuadraticGraphics/Inequalities-13.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-13.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-10.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-10.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-11.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-11.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-12.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-12.pdf" > [148]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 223--224
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 223--224

 []


Underfull \hbox (badness 1107) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 interval to construct the sign diagram.
 []


Underfull \hbox (badness 2582) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 You’ll get the same sign chart if you
 []

File: figures/LinearQuadraticGraphics/Inequalities-14.pdf Graphic file (type QT
m)
<use  "figures/LinearQuadraticGraphics/Inequalities-14.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-15.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-15.pdf" >
Underfull \hbox (badness 1953) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 3.40: |Verifying the solution to
 []

[149]
File: figures/LinearQuadraticGraphics/Inequalities-16.pdf Graphic file (type QT
m)
 <use  "figures/LinearQuadraticGraphics/Inequalities-16.pdf" >
Overfull \hbox (9.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/LinearQuadraticGraphics/Inequalities-17.pdf Graphic file (type QT
m)
<use  "figures/LinearQuadraticGraphics/Inequalities-17.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-18.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-18.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-19.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-19.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-20.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-20.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-21.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-21.pdf" > [150]
File: figures/LinearQuadraticGraphics/Inequalities-22.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-22.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-23.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-23.pdf" > [151]
File: figures/LinearQuadraticGraphics/Inequalities-24.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-24.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-25.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-25.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-26.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-26.pdf" > [152]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [153

]
Missing character: There is no ϵ in font [cmmi10]/I/OT:mapping=tex-text;!
Missing character: There is no ϵ in font [cmmi10]/I/OT:mapping=tex-text;!

[154])
Chapter 4.
(text_pre/03_GraphsofPolynomials.tex
Overfull \hbox (0.89142pt too wide) in paragraph at lines 4--5
\EU1/Calibri(0)/m/n/10 Three of the families of functions studied thus far – co
nstant, linear and quadratic
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 10--11
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 10--11

 []

[155




]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 82--83
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 82--83

 []


Underfull \hbox (badness 1406) has occurred while \output is active
[][]$ \EU1/Calibri(0)/m/n/9 are known as \EU1/Calibri(0)/m/it/9 indeterminant f
orms\EU1/Calibri(0)/m/n/9 .
 []

[156]
File: figures/PolynomialsGraphics/GraphsofPolynomials-1.pdf Graphic file (type 
QTm)
 <use  "figures/PolynomialsGraphics/GraphsofPolynomials-1.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-2.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-2.pdf" > [157]
File: figures/PolynomialsGraphics/GraphsofPolynomials-6.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-6.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-7.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-7.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 222--223
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 222--223

 []

File: figures/PolynomialsGraphics/BoxNoTopV.png Graphic file (type QTm)
<use  "figures/PolynomialsGraphics/BoxNoTopV.png" >
File: figures/PolynomialsGraphics/BoxNoTopVmax.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/BoxNoTopVmax.png" >
Overfull \hbox (16.13214pt too wide) has occurred while \output is active
 [][] 
 []

[158]
File: figures/PolynomialsGraphics/GraphsofPolynomials-11.pdf Graphic file (type
 QTm)
 <use  "figures/PolynomialsGraphics/GraphsofPolynomials-11.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-12.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-12.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 282--283
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 282--283

 []

File: figures/PolynomialsGraphics/GraphsofPolynomials-3.pdf Graphic file (type 
QTm)
<use  "figures/PolynomialsGraphics/GraphsofPolynomials-3.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-4.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-4.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-5.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-5.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-8.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-8.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-9.pdf Graphic file (type 
QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-9.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-10.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-10.pdf" > [159]
Overfull \hbox (1.95032pt too wide) in paragraph at lines 297--298
[]\EU1/Calibri(0)/m/n/10 The notion of smoothness is what tells us graphically 
that, for example, $[]\OT1/cmr/m/n/10 ([]) =
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 303--304
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 303--304

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 338--339
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 338--339

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/PolynomialsGraphics/GraphsofPolynomials-13.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-13.pdf" >
Overfull \hbox (4.99962pt too wide) has occurred while \output is active
 [][][] 
 []


Underfull \hbox (badness 2134) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 4.5: |Pathologies not found on
 []

File: figures/PolynomialsGraphics/GraphsofPolynomials-14.pdf Graphic file (type
 QTm)
<use  "figures/PolynomialsGraphics/GraphsofPolynomials-14.pdf" > [160]
Overfull \hbox (16.45343pt too wide) in paragraph at lines 351--351
[]$[]$ \EU1/Calibri(0)/m/n/10 First, we find the zeros of $[]$ by solving $[][]
\OT1/cmr/m/n/10 ([] \OMS/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 )[]([] + []) [] =
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 361--362
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 361--362

 []

File: figures/PolynomialsGraphics/GraphsofPolynomials-15.pdf Graphic file (type
 QTm)
<use  "figures/PolynomialsGraphics/GraphsofPolynomials-15.pdf" >
Overfull \hbox (9.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/PolynomialsGraphics/GraphsofPolynomials-16.pdf Graphic file (type
 QTm)
<use  "figures/PolynomialsGraphics/GraphsofPolynomials-16.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[161]
File: figures/PolynomialsGraphics/EndBehaviour_near.png Graphic file (type QTm)

 <use  "figures/PolynomialsGraphics/EndBehaviour_near.png" >
File: figures/PolynomialsGraphics/EndBehaviour_far.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/EndBehaviour_far.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[162]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 412--413
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 412--413

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 430--431
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 430--431

 []


Overfull \hbox (2.2511pt too wide) in paragraph at lines 434--435
[]\EU1/Calibri(0)/m/n/10 Our last example shows how end behaviour and multiplic
ity allow us to sketch
 []

File: figures/PolynomialsGraphics/GraphsofPolynomials-19.pdf Graphic file (type
 QTm)
<use  "figures/PolynomialsGraphics/GraphsofPolynomials-19.pdf" > [163]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

Requested font "Calibri/BI/OT:script=latn;language=DFLT;mapping=tex-text;mappin
g=tex-text;" at 9.0pt
 -> C:/WINDOWS/Fonts/calibriz.ttf
 [164

]
File: figures/PolynomialsGraphics/GraphsofPolynomials-20.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-20.pdf" > [165])
(text_pre/03_Polydivision.tex
Overfull \hbox (0.42805pt too wide) in paragraph at lines 1--1
[]\EU1/Calibri(0)/bx/n/14.4 The Factor Theorem and the Remainder Theorem 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 39--40
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 39--40

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 49--50
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 49--50

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/PolynomialsGraphics/CubicIrrRootZeros.png Graphic file (type QTm)


<use  "figures/PolynomialsGraphics/CubicIrrRootZeros.png" >
Overfull \hbox (20.99957pt too wide) has occurred while \output is active
 [][][] 
 []

[166

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 60--61
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 60--61

 []

[167] [168]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 250--251
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 250--251

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 274--275
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 274--275

 []

[169]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [170

]) (text_pre/03_RealZeros.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 30--30
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 30--30

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 40--41
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 40--41

 []

[171

]
File: figures/PolynomialsGraphics/RealZero1.png Graphic file (type QTm)
 <use  "figures/PolynomialsGraphics/RealZero1.png" > [172]
File: figures/PolynomialsGraphics/RealZero2.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/RealZero2.png" > [173]
File: figures/PolynomialsGraphics/RealZero3.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/RealZero3.png" >
File: figures/PolynomialsGraphics/RealZero4.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/RealZero4.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[174] [175]
Underfull \hbox (badness 10000) in paragraph at lines 567--567

 []

File: figures/PolynomialsGraphics/RealZeros_New-1.pdf Graphic file (type QTm)
<use  "figures/PolynomialsGraphics/RealZeros_New-1.pdf" >
Underfull \hbox (badness 4266) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 We don’t use the word “impossible”
 []

[176]
File: figures/PolynomialsGraphics/RealZeros_New-2.pdf Graphic file (type QTm)
 <use  "figures/PolynomialsGraphics/RealZeros_New-2.pdf" > [177]
Overfull \hbox (3.09503pt too wide) in paragraph at lines 606--606
\EU1/Calibri(0)/m/n/10 factor out the $\OMS/cmsy/m/n/10 ^^@[]$ \EU1/Calibri(0)/
m/n/10 common to all the coefficients to get $\OMS/cmsy/m/n/10 ^^@[] [] \OML/cm
m/m/it/10 >
 []

File: figures/PolynomialsGraphics/RealZero5.png Graphic file (type QTm)
<use  "figures/PolynomialsGraphics/RealZero5.png" >
File: figures/PolynomialsGraphics/RealZero6.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/RealZero6.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/PolynomialsGraphics/RealZeros_New-3.pdf Graphic file (type QTm)
<use  "figures/PolynomialsGraphics/RealZeros_New-3.pdf" >
File: figures/PolynomialsGraphics/RealZero7.png Graphic file (type QTm)

<use  "figures/PolynomialsGraphics/RealZero7.png" > [178]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [179

] [180])
(text_pre/03_ComplexZeros.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 14--15
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 14--15

 []


Underfull \hbox (badness 2326) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The Fundamental Theorem of Algebra
 []

[181

]
Underfull \hbox (badness 1845) in paragraph at lines 30--30
\EU1/Calibri(0)/m/n/10 If the degree of $[]$ is $[]$ and $[] \OMS/cmsy/m/n/10 ^
^U []$\EU1/Calibri(0)/m/n/10 , then $[]$ has exactly $[]$ com-
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 30--31
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 30--31

 []


Overfull \hbox (2.79843pt too wide) in paragraph at lines 116--116
\EU1/Calibri(0)/m/n/10 function. At that point, we can find the remaining zeros
 using the Quadratic
 []


Underfull \hbox (badness 6188) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 We don’t really recommend jumping
 []

[182]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 127--128
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 127--128

 []

[183]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 150--151
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 150--151

 []

[184] [185] [186]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [187

]) [188



]
Chapter 5.
(text_pre/04_IntroRational.tex
Overfull \hbox (0.16711pt too wide) in paragraph at lines 4--5
\EU1/Calibri(0)/m/n/10 arithmetic rules defined in Section []2.4[], we will pro
duce another polynomial func-
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 13--14
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 13--14

 []


Underfull \hbox (badness 1205) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 According to Definition []40[], all polyno-
 []

[189

] [190]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 147--148
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 147--148

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 151--152
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 151--152

 []

File: figures/RationalsGraphics/Rationals01.png Graphic file (type QTm)
<use  "figures/RationalsGraphics/Rationals01.png" >
Overfull \hbox (2.45236pt too wide) has occurred while \output is active
 $[]$ 
 []

[191]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 207--209
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 207--209

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/RationalsGraphics/IntroRational-1.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/IntroRational-1.pdf" > [192]
File: figures/RationalsGraphics/Rationals02.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals02.png" >
File: figures/RationalsGraphics/Rationals03.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals03.png" >
File: figures/RationalsGraphics/Rationals04.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals04.png" >
File: figures/RationalsGraphics/Rationals05.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals05.png" > [193]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 315--316
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 315--316

 []


Underfull \vbox (badness 7704) has occurred while \output is active []

File: figures/RationalsGraphics/Doomsday.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Doomsday.png" > [194]
Underfull \vbox (badness 10000) has occurred while \output is active []

 [195]
File: figures/RationalsGraphics/Rationals06.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals06.png" >
File: figures/RationalsGraphics/Rationals07.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals07.png" >
File: figures/RationalsGraphics/Rationals08.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals08.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[196]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 452--453
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 452--453

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 464--465
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 464--465

 []


Underfull \vbox (badness 1648) has occurred while \output is active []

File: figures/RationalsGraphics/SA01.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/SA01.png" >
File: figures/RationalsGraphics/SA02.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/SA02.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[197]
File: figures/RationalsGraphics/SAEX01.png Graphic file (type QTm)
 <use  "figures/RationalsGraphics/SAEX01.png" >
File: figures/RationalsGraphics/SAEX02.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/SAEX02.png" > [198]
File: figures/RationalsGraphics/SAEX03.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/SAEX03.png" > [199]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [200

])
(text_pre/04_RationalGraphs.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 39--40
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 39--40

 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 1681) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Recall that at this stage (prior to dis-
 []


Underfull \hbox (badness 1122) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 cussing calculus), continuity of a func-
 []

File: figures/RationalsGraphics/RationalGraphs-1.pdf Graphic file (type QTm)
<use  "figures/RationalsGraphics/RationalGraphs-1.pdf" >
File: figures/RationalsGraphics/RationalGraphs-2.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-2.pdf" >
Underfull \hbox (badness 1024) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 5.20: |The sign diagram for the
 []

[201

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 65--66
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 65--66

 []

[202] [203]
File: figures/RationalsGraphics/RationalGraphs-3.pdf Graphic file (type QTm)
 <use  "figures/RationalsGraphics/RationalGraphs-3.pdf" >
File: figures/RationalsGraphics/RationalGraphs-4.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-4.pdf" >
File: figures/RationalsGraphics/RationalGraphs-5.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-5.pdf" >
File: figures/RationalsGraphics/RationalGraphs-6.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-6.pdf" > [204] [205]
Overfull \hbox (0.26819pt too wide) in paragraph at lines 209--209
[]\EU1/Calibri(0)/m/n/10 Since the degrees of the numerator and denominator of 
$[]\OT1/cmr/m/n/10 ([])$ \EU1/Calibri(0)/m/n/10 are the same,
 []

File: figures/RationalsGraphics/RationalGraphs-7.pdf Graphic file (type QTm)
<use  "figures/RationalsGraphics/RationalGraphs-7.pdf" >
File: figures/RationalsGraphics/RationalGraphs-8.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-8.pdf" >
File: figures/RationalsGraphics/RationalGraphs-9.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-9.pdf" > [206]
Overfull \hbox (0.19537pt too wide) in paragraph at lines 268--268
[] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@[]$\EU1/Calibri(0)/m/n/10 . To make th
is exclusion specific, we write $[]\OT1/cmr/m/n/10 ([]) = []$\EU1/Calibri(0)/m/
n/10 ,
 []

File: figures/RationalsGraphics/RationalGraphs-10.pdf Graphic file (type QTm)
<use  "figures/RationalsGraphics/RationalGraphs-10.pdf" > [207]
File: figures/RationalsGraphics/RationalGraphs-11.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-11.pdf" >
File: figures/RationalsGraphics/RationalGraphs-12.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-12.pdf" >
File: figures/RationalsGraphics/RationalGraphs-13.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-13.pdf" >
File: figures/RationalsGraphics/RationalGraphs-14.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-14.pdf" > [208]
Overfull \hbox (12.82013pt too wide) in paragraph at lines 310--311
[]\EU1/Calibri(0)/m/n/10 As usual, the authors offer no apologies for what may 
be construed as ‘pedantry’
 []

File: figures/RationalsGraphics/RationalGraphs-15.pdf Graphic file (type QTm)
<use  "figures/RationalsGraphics/RationalGraphs-15.pdf" >
File: figures/RationalsGraphics/RationalGraphs-16.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-16.pdf" >
File: figures/RationalsGraphics/Rationals09.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals09.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[209]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [210

]) (text_pre/04_RationalIneq.tex
Underfull \hbox (badness 10000) in paragraph at lines 72--72

 []

[211

]
Overfull \hbox (1.70891pt too wide) detected at line 144
[]
 []

File: figures/RationalsGraphics/RationalIneq-1.pdf Graphic file (type QTm)
<use  "figures/RationalsGraphics/RationalIneq-1.pdf" >
File: figures/RationalsGraphics/Rationals10.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals10.png" >
File: figures/RationalsGraphics/Rationals11.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals11.png" > [212] [213] [214]
File: figures/RationalsGraphics/RationalIneq-2.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalIneq-2.pdf" > [215]
File: figures/RationalsGraphics/RationalIneq-3.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalIneq-3.pdf" > [216]
File: figures/RationalsGraphics/RationalIneq-4.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalIneq-4.pdf" >
File: figures/RationalsGraphics/Rationals12.png Graphic file (type QTm)

<use  "figures/RationalsGraphics/Rationals12.png" > [217]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 338--339
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 338--339

 []

[218] [219]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [220

] [221]) [222



]
Chapter 6.
(text_pre/05_FunctionComposition.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 12--13
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 12--13

 []

File: figures/FurtherGraphics/FunctionComposition-1.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/FunctionComposition-1.pdf" > [223

]
File: figures/FurtherGraphics/FunctionComposition-2.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/FunctionComposition-2.pdf" > [224] [225]
Underfull \vbox (badness 4927) has occurred while \output is active []

File: figures/FurtherGraphics/FunctionComposition-3.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/FunctionComposition-3.pdf" > [226] [227]
[228]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 285--286
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 285--286

 []

[229] [230] [231]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [232

]
Overfull \hbox (14.46515pt too wide) detected at line 329
[] \OT1/cmr/m/n/9 = \OMS/cmsy/m/n/9 f\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/
cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^@[]\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/
n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ;
 \OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^@[]\O
T1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/
m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; \OMS/cmsy/m/n/9 ^^
@[]\OT1/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1
/cmr/m/n/9 )\OML/cmm/m/it/9 ; \OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; []\OT1/cmr/m/
n/9 )\OMS/cmsy/m/n/9 g\OML/cmm/m/it/9 :
 []

File: figures/FurtherGraphics/FunctionComposition-4.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/FunctionComposition-4.pdf" >
File: figures/FurtherGraphics/FunctionComposition-5.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/FunctionComposition-5.pdf" >
Overfull \hbox (1.48386pt too wide) in paragraph at lines 329--329
 [] 
 []

[233]) (text_pre/05_InverseFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 45--46
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 45--46

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 64--65
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 64--65

 []

File: figures/FurtherGraphics/InverseFunctions-1.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/InverseFunctions-1.pdf" > [234

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 92--93
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 92--93

 []

File: figures/FurtherGraphics/InverseFunctions-2.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/InverseFunctions-2.pdf" >
Underfull \hbox (badness 2261) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 tion composition standpoint, however,
 []

[235]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 122--123
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 122--123

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 131--132
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 131--132

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 152--153
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 152--153

 []

File: figures/FurtherGraphics/InverseFunctions-3.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/InverseFunctions-3.pdf" >
File: figures/FurtherGraphics/InverseFunctions-4.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-4.pdf" >
File: figures/FurtherGraphics/InverseFunctions-5.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-5.pdf" > [236]
File: figures/FurtherGraphics/InverseFunctions-6.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-6.pdf" > [237]
Overfull \hbox (12.38034pt too wide) detected at line 254
[]
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 273--274
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 273--274

 []

File: figures/FurtherGraphics/InverseFunctions-7.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/InverseFunctions-7.pdf" >
File: figures/FurtherGraphics/InverseFunctions-8.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-8.pdf" >
File: figures/FurtherGraphics/InverseFunctions-9.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-9.pdf" > [238] [239]
File: figures/FurtherGraphics/InverseFunctions-10.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-10.pdf" > [240]
Underfull \vbox (badness 1184) has occurred while \output is active []

File: figures/FurtherGraphics/InverseFunctions-11.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-11.pdf" >
File: figures/FurtherGraphics/InverseFunctions-12.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-12.pdf" >
File: figures/FurtherGraphics/InverseFunctions-13.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-13.pdf" > [241]
File: figures/FurtherGraphics/InverseFunctions-14.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-14.pdf" >
File: figures/FurtherGraphics/InverseFunctions-15.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-15.pdf" > [242]
File: figures/FurtherGraphics/InverseFunctions-16.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-16.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/FurtherGraphics/InverseFunctions-17.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/InverseFunctions-17.pdf" >
File: figures/FurtherGraphics/InverseFunctions-18.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/InverseFunctions-18.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[243]
Overfull \hbox (5.2894pt too wide) in paragraph at lines 572--572
[]\EU1/Calibri(0)/m/n/10 We compute $[] \OT1/cmr/m/n/10 ([]) = [] [] = [] [] = 
\OMS/cmsy/m/n/10 ^^@[]\OML/cmm/m/it/10 :[] [][] \OT1/cmr/m/n/10 +
 []


Overfull \hbox (0.3342pt too wide) in paragraph at lines 572--572
[]\EU1/Calibri(0)/m/n/10 We know from Section []3.3[] that the graph of $[] \OT
1/cmr/m/n/10 = [] ([])$ \EU1/Calibri(0)/m/n/10 is a parabola
 []

[244]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [245

]) (text_pre/05_AlgebraicFunctions.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 10--11
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 10--11

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 64--65
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 64--65

 []

File: figures/FurtherGraphics/AlgebraicFunctions-1.pdf Graphic file (type QTm)
<use  "figures/FurtherGraphics/AlgebraicFunctions-1.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-2.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-2.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-3.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-3.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-4.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-4.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-5.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-5.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-6.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-6.pdf" > [246

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 81--82
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 81--82

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 110--111
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 110--111

 []


Underfull \vbox (badness 2326) has occurred while \output is active []


Underfull \hbox (badness 1648) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 As mentioned in Section []3.2[], $[]\OT1/cmr/m/n/9 ([])
 =
 []

[247]
File: figures/FurtherGraphics/AlgebraicFunctions-7.pdf Graphic file (type QTm)
 <use  "figures/FurtherGraphics/AlgebraicFunctions-7.pdf" >
File: figures/FurtherGraphics/Algebraic01.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic01.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[248]
File: figures/FurtherGraphics/AlgebraicFunctions-8.pdf Graphic file (type QTm)
 <use  "figures/FurtherGraphics/AlgebraicFunctions-8.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-9.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-9.pdf" >
File: figures/FurtherGraphics/Algebraic02.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic02.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/FurtherGraphics/AlgebraicFunctions-10.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-10.pdf" >
File: figures/FurtherGraphics/Algebraic03.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic03.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/FurtherGraphics/AlgebraicFunctions-11.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-11.pdf" > [249]
File: figures/FurtherGraphics/AlgebraicFunctions-12.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-12.pdf" >
File: figures/FurtherGraphics/Algebraic04.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic04.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[250]
Overfull \hbox (8.23042pt too wide) in paragraph at lines 318--318
\EU1/Calibri(0)/m/n/10 Setting the denominator equal to zero we get $\OT1/cmr/m
/n/10 ([] \OMS/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 )[] = []$\EU1/Calibri(0)/m/n/1
0 , or $[] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (28.89302pt too wide) detected at line 318
[]
 []


Overfull \hbox (34.1399pt too wide) detected at line 318
[]
 []

File: figures/FurtherGraphics/AlgebraicFunctions-13.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-13.pdf" >
File: figures/FurtherGraphics/Algebraic05.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic05.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/FurtherGraphics/Algebraic06.png Graphic file (type QTm)
<use  "figures/FurtherGraphics/Algebraic06.png" >
File: figures/FurtherGraphics/Algebraic07.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic07.png" > [251]
File: figures/FurtherGraphics/AlgebraicFunctions-14.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-14.pdf" >
File: figures/FurtherGraphics/Algebraic08.png Graphic file (type QTm)

<use  "figures/FurtherGraphics/Algebraic08.png" >
Overfull \hbox (23.79793pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/FurtherGraphics/AlgebraicFunctions-15.pdf Graphic file (type QTm)

<use  "figures/FurtherGraphics/AlgebraicFunctions-15.pdf" > [252] [253]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


[254

] [255]) [256



]
Chapter 7.
(text_pre/06_IntroExpLogs.tex
Overfull \hbox (6.76553pt too wide) in paragraph at lines 1--1
[]\EU1/Calibri(0)/bx/n/14.4 Introduction to Exponential and Logarithmic Func-
 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 5924) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Exponential and logarithmic functions
 []


Underfull \hbox (badness 1077) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 tial equations, which are used to pro-
 []

File: figures/ExpLogsGraphics/IntroExpLogs-1.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/IntroExpLogs-1.pdf" >
Underfull \hbox (badness 2772) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 To fully understand the argument we
 []

[257

]
Requested font "Calibri/BI/OT:script=latn;language=DFLT;mapping=tex-text;mappin
g=tex-text;" at 10.0pt
 -> C:/WINDOWS/Fonts/calibriz.ttf

Overfull \hbox (1.39998pt too wide) in paragraph at lines 44--45
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 44--45

 []

File: figures/ExpLogsGraphics/IntroExpLogs-4.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/IntroExpLogs-4.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-5.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-5.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 127--128
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 127--128

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/ExpLogsGraphics/IntroExpLogs-2.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-2.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-3.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-3.pdf" > [258] [259]
File: figures/ExpLogsGraphics/IntroExpLogs-6.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-6.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-7.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-7.pdf" > [260]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 220--221
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 220--221

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 230--231
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 230--231

 []

File: figures/ExpLogsGraphics/IntroExpLogs-8.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/IntroExpLogs-8.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-9.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-9.pdf" > [261]
File: figures/ExpLogsGraphics/IntroExpLogs-12.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-12.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-13.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-13.pdf" >
Overfull \hbox (31.39998pt too wide) in paragraph at lines 312--313
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 312--313

 []

File: figures/ExpLogsGraphics/IntroExpLogs-10.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/IntroExpLogs-10.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-11.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-11.pdf" > [262]
Overfull \hbox (11.44408pt too wide) in paragraph at lines 364--364
\EU1/Calibri(0)/m/n/10 as a power of $[][]$. We have $[]\OML/cmm/m/it/10 :[][][
] \OT1/cmr/m/n/10 = [] = [] = [][][]$\EU1/Calibri(0)/m/n/10 . Hence, $[]\OT1/cm
r/m/n/10 ([]\OML/cmm/m/it/10 :[][][]\OT1/cmr/m/n/10 ) =
 []

[263]
Overfull \hbox (1.97113pt too wide) in paragraph at lines 402--403
[]\EU1/Calibri(0)/m/n/10 While logarithms have some interesting applications of
 their own which you’ll
 []

File: figures/ExpLogsGraphics/ExpLogs01.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs01.png" >
Overfull \hbox (11.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/IntroExpLogs-14.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/IntroExpLogs-14.pdf" >
File: figures/ExpLogsGraphics/ExpLogs02.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs02.png" >
Overfull \hbox (13.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[264]
File: figures/ExpLogsGraphics/IntroExpLogs-15.pdf Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/IntroExpLogs-15.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-16.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-16.pdf" > [265]
File: figures/ExpLogsGraphics/IntroExpLogs-17.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-17.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-18.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-18.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-19.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-19.pdf" >
Overfull \hbox (8.9996pt too wide) has occurred while \output is active
 [][][] 
 []

[266]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [267

] [268] [269]) (text_pre/06_LogProperties.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 20--21
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 20--21

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 37--38
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 37--38

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 56--57
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 56--57

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [270

]
Underfull \hbox (badness 1527) in paragraph at lines 75--75
[]\EU1/Calibri(0)/bx/n/10 Quotient Rule: []$[] [] \OT1/cmr/m/n/10 = []([]) \OMS
/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 ([])$\EU1/Calibri(0)/m/n/10 . In other words
,
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 75--76
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 75--76

 []

[271]
Underfull \hbox (badness 6001) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Interestingly enough, expanding loga-
 []


Underfull \hbox (badness 6141) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 rithms is the exact \EU1/Calibri(0)/m/it/9 opposite \EU1/
Calibri(0)/m/n/9 process
 []

[272] [273] [274]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 255--256
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 255--256

 []

[275]
Underfull \hbox (badness 1062) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 While, in the grand scheme of things,
 []

File: figures/ExpLogsGraphics/ExpLogs03.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs03.png" >
Overfull \hbox (12.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs04.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs04.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[276]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [277

] [278]) (text_pre/06_ExpEquations.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 41--42
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 41--42

 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 2027) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Please resist the temptation to divide
 []

[279

]
File: figures/ExpLogsGraphics/ExpLogs05.png Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/ExpLogs05.png" >
Overfull \hbox (5.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs06.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs06.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs07.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs07.png" >
Overfull \hbox (12.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs08.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs08.png" >
Overfull \hbox (15.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[280]
File: figures/ExpLogsGraphics/ExpLogs09.png Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/ExpLogs09.png" >
Overfull \hbox (12.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs10.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs10.png" >
Overfull \hbox (15.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[281]
File: figures/ExpLogsGraphics/ExpEquations-1.pdf Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/ExpEquations-1.pdf" >
File: figures/ExpLogsGraphics/ExpLogs11.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs11.png" >
Overfull \hbox (22.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpEquations-2.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpEquations-2.pdf" >
File: figures/ExpLogsGraphics/ExpLogs12.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs12.png" >
Overfull \hbox (20.9996pt too wide) has occurred while \output is active
 [][][] 
 []

[282]
Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/ExpLogsGraphics/ExpEquations-3.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpEquations-3.pdf" >
File: figures/ExpLogsGraphics/ExpLogs13.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs13.png" >
Overfull \hbox (23.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpEquations-4.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpEquations-4.pdf" >
File: figures/ExpLogsGraphics/ExpEquations-5.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpEquations-5.pdf" > [283]
File: figures/ExpLogsGraphics/ExpLogs14.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs14.png" >
Overfull \hbox (11.9996pt too wide) has occurred while \output is active
 [][][] 
 []

[284]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [285

] [286]) (text_pre/06_LogEquations.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 25--26
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 25--26

 []


Overfull \hbox (1.69727pt too wide) in paragraph at lines 121--121
[]$[][]\OT1/cmr/m/n/10 ([] \OMS/cmsy/m/n/10 ^^@ [][]\OT1/cmr/m/n/10 ) = [][] []
$ 
 []

File: figures/ExpLogsGraphics/ExpLogs15.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs15.png" >
Overfull \hbox (11.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs16.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs16.png" >
Overfull \hbox (15.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[287

]
File: figures/ExpLogsGraphics/ExpLogs17.png Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/ExpLogs17.png" >
Overfull \hbox (11.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs18.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs18.png" >
Overfull \hbox (11.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs19.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs19.png" >
Overfull \hbox (12.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs20.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs20.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[288]
Underfull \hbox (badness 10000) in paragraph at lines 222--222
[]$[][] \OML/cmm/m/it/10 <
 []

File: figures/ExpLogsGraphics/LogEquations-1.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/LogEquations-1.pdf" >
File: figures/ExpLogsGraphics/ExpLogs21.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs21.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/LogEquations-2.pdf Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/LogEquations-2.pdf" >
File: figures/ExpLogsGraphics/ExpLogs22.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs22.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[289]
Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/ExpLogsGraphics/LogEquations-3.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/LogEquations-3.pdf" >
File: figures/ExpLogsGraphics/ExpLogs23.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs23.png" >
Overfull \hbox (8.66666pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs24.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs24.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[290]
File: figures/ExpLogsGraphics/ExpLogs25.png Graphic file (type QTm)
 <use  "figures/ExpLogsGraphics/ExpLogs25.png" >
Overfull \hbox (13.99959pt too wide) has occurred while \output is active
 [][][] 
 []

[291]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [292

] [293]) (text_pre/06_ExpLogApplications.tex
Overfull \hbox (5.79524pt too wide) in paragraph at lines 1--1
[]\EU1/Calibri(0)/bx/n/14.4 Applications of Exponential and Logarithmic Func-
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 15--16
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 15--16

 []

[294

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 24--25
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 24--25

 []


Overfull \hbox (14.68224pt too wide) in paragraph at lines 60--60
\EU1/Calibri(0)/m/n/10 Suppose $\OT1/cmr/m/n/10 $[][][][]$ \EU1/Calibri(0)/m/n/
10 is invested in an account which offers $[]\OML/cmm/m/it/10 :[][][]\OT1/cmr/m
/n/10 %$ \EU1/Calibri(0)/m/n/10 compounded monthly. 
 []

[295]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 86--87
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 86--87

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 95--96
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 95--96

 []

[296]
Overfull \hbox (4.08012pt too wide) in paragraph at lines 99--100
\EU1/Calibri(0)/m/n/10 tinuously compounding gives $[]\OT1/cmr/m/n/10 ([][]) = 
[][][][][][]$ \EU1/Calibri(0)/m/n/10 which is about $\OT1/cmr/m/n/10 $[][]\OML/
cmm/m/it/10 ;  [][][]:[][]$
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 112--113
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 112--113

 []

[297]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 133--134
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 133--134

 []


Overfull \hbox (1.61566pt too wide) in paragraph at lines 139--140
[]$[]$ \EU1/Calibri(0)/m/n/10 Since we start with $[]$ grams initially, Equatio
n []33[] gives $[]\OT1/cmr/m/n/10 ([]) =
 []

[298]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 152--153
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 152--153

 []


Underfull \hbox (badness 6859) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The Second Law of Thermodynamics
 []

[299]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 191--192
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 191--192

 []

[300]
Underfull \vbox (badness 2809) has occurred while \output is active []

File: figures/ExpLogsGraphics/ExpLogs26.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs26.png" >
Overfull \hbox (8.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs27.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs27.png" >
Overfull \hbox (8.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/ExpLogsGraphics/ExpLogs28.png Graphic file (type QTm)
<use  "figures/ExpLogsGraphics/ExpLogs28.png" >
File: figures/ExpLogsGraphics/ExpLogs29.png Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/ExpLogs29.png" > [301]
Overfull \hbox (4.87703pt too wide) in paragraph at lines 286--287
[]$[]$ \EU1/Calibri(0)/m/n/10 We set $[] \OT1/cmr/m/n/10 = []\OML/cmm/m/it/10 :
[]$ \EU1/Calibri(0)/m/n/10 and get $[]\OML/cmm/m/it/10 :[] \OT1/cmr/m/n/10 = []
\OML/cmm/m/it/10 :[] \OT1/cmr/m/n/10 + [] []$\EU1/Calibri(0)/m/n/10 , or $[] []
 \OT1/cmr/m/n/10 =
 []


Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The equation for blood pH in Ex-
 []


Underfull \hbox (badness 10000) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 ample []133[] is derived from the
 []


Underfull \hbox (badness 10000) has occurred while \output is active
[]$[]$[]\EU1/Calibri(0)/m/n/9 .
 []


Underfull \hbox (badness 1953) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 See Exercise []43[] in Section []7.2[]. Has-
 []


Underfull \hbox (badness 4819) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 selbalch himself was studying carbon
 []

[302]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

Requested font "Calibri/B/OT:script=latn;language=DFLT;mapping=tex-text;mapping
=tex-text;" at 6.0pt
 -> C:/WINDOWS/Fonts/calibrib.ttf
 [303

] [304] [305]) [306



]
Chapter 8.
(text_pre/07_Angles.tex
File: figures/IntroTrigGraphics/Angles-2.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/Angles-2.pdf" >
File: figures/IntroTrigGraphics/Angles-3.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-3.pdf" >
Overfull \hbox (15.0pt too wide) in paragraph at lines 15--25
[]$[]$ 
 []

File: figures/IntroTrigGraphics/Angles-4.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-4.pdf" >
File: figures/IntroTrigGraphics/Angles-5.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-5.pdf" >
Overfull \hbox (15.0pt too wide) in paragraph at lines 33--43
[]$[]$ 
 []

File: figures/IntroTrigGraphics/Angles-9.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-9.pdf" >
File: figures/IntroTrigGraphics/Angles-10.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-10.pdf" >
File: figures/IntroTrigGraphics/Angles-11.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-11.pdf" >
Overfull \hbox (4.00293pt too wide) in paragraph at lines 70--77
[][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 69--80

 []


Underfull \vbox (badness 2495) has occurred while \output is active []

File: figures/IntroTrigGraphics/Angles-1.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-1.pdf" >
File: figures/IntroTrigGraphics/Angles-6.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-6.pdf" >
File: figures/IntroTrigGraphics/Angles-7.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-7.pdf" >
File: figures/IntroTrigGraphics/Angles-8.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-8.pdf" >
Underfull \hbox (badness 2142) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The choice of ‘$[][][]$’ is most often at-
 []

[307

]
File: figures/IntroTrigGraphics/Angles-12.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/Angles-12.pdf" >
File: figures/IntroTrigGraphics/Angles-13.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-13.pdf" >
File: figures/IntroTrigGraphics/Angles-14.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-14.pdf" >
Overfull \hbox (4.00293pt too wide) in paragraph at lines 90--97
[][]
 []

File: figures/IntroTrigGraphics/Angles-15.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-15.pdf" >
File: figures/IntroTrigGraphics/Angles-16.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-16.pdf" >
Overfull \hbox (11.99963pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/IntroTrigGraphics/Angles-17.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-17.pdf" >
File: figures/IntroTrigGraphics/Angles-18.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-18.pdf" >
File: figures/IntroTrigGraphics/Angles-19.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-19.pdf" > [308]
File: figures/IntroTrigGraphics/Angles-20.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-20.pdf" >
File: figures/IntroTrigGraphics/Angles-21.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-21.pdf" >
File: figures/IntroTrigGraphics/Angles-22.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-22.pdf" >
File: figures/IntroTrigGraphics/Angles-23.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-23.pdf" > [309]
Requested font "[cmmi10]/B/OT:mapping=tex-text;" at 10.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/B/OT:mapping=tex-text;" at 7.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/B/OT:mapping=tex-text;" at 5.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb

Overfull \hbox (1.39998pt too wide) in paragraph at lines 197--198
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--198

 []

File: figures/IntroTrigGraphics/Angles-24.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-24.pdf" >
File: figures/IntroTrigGraphics/Angles-25.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-25.pdf" >
File: figures/IntroTrigGraphics/Angles-26.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-26.pdf" >
File: figures/IntroTrigGraphics/Angles-27.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-27.pdf" >
Overfull \hbox (21.29851pt too wide) has occurred while \output is active
 [][][] 
 []

[310]
File: figures/IntroTrigGraphics/Angles-28.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/Angles-28.pdf" >
File: figures/IntroTrigGraphics/Angles-29.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-29.pdf" >
File: figures/IntroTrigGraphics/Angles-30.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-30.pdf" >
File: figures/IntroTrigGraphics/Angles-31.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-31.pdf" > [311]
Underfull \hbox (badness 2875) in paragraph at lines 282--282
[]\EU1/Calibri(0)/m/n/10 To convert degree measure to radian measure, multiply 
by
 []


Underfull \hbox (badness 2875) in paragraph at lines 282--282
[]\EU1/Calibri(0)/m/n/10 To convert radian measure to degree measure, multiply 
by
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 282--283
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 282--283

 []

File: figures/IntroTrigGraphics/Angles-32.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-32.pdf" >
File: figures/IntroTrigGraphics/Angles-33.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-33.pdf" >
File: figures/IntroTrigGraphics/Angles-34.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-34.pdf" >
Overfull \hbox (150.0pt too wide) in paragraph at lines 291--301
$[]$ 
 []

[312]
File: figures/IntroTrigGraphics/Angles-35.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/Angles-35.pdf" >
File: figures/IntroTrigGraphics/Angles-36.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-36.pdf" >
File: figures/IntroTrigGraphics/Angles-37.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-37.pdf" > [313]
File: figures/IntroTrigGraphics/Angles-38.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-38.pdf" >
File: figures/IntroTrigGraphics/Angles-39.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-39.pdf" > [314] [315]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

Requested font "[cmmi10]/B/OT:mapping=tex-text;" at 9.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/B/OT:mapping=tex-text;" at 6.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
 [316

]
Underfull \hbox (badness 10000) in paragraph at lines 379--379
[]\EU1/Calibri(0)/m/n/9 (Hint: Use the proportion $[] \OT1/cmr/m/n/9 =
 []

File: figures/IntroTrigGraphics/Angles-40.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Angles-40.pdf" > [317])
(text_pre/07_TheUnitCircle.tex
File: figures/IntroTrigGraphics/TheUnitCircle-5.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-5.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-6.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-6.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 96--96
[][]
 []


Overfull \hbox (5.00003pt too wide) in paragraph at lines 96--96
 $[]$ 
 []


Underfull \vbox (badness 6725) has occurred while \output is active []

File: figures/IntroTrigGraphics/TheUnitCircle-2.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-2.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-3.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-3.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.30: |Finding $[]\OT1/cmr/m/n/9 ([][][][])$ \EU
1/Calibri(0)/m/n/9 and
 []

File: figures/IntroTrigGraphics/TheUnitCircle-4.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-4.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.31: |Finding $[]\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/
9 ^^@[]\OT1/cmr/m/n/9 )$ \EU1/Calibri(0)/m/n/9 and
 []

[318

]
File: figures/IntroTrigGraphics/TheUnitCircle-7.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-7.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-8.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-8.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 96--96
[][]
 []


Overfull \hbox (5.00003pt too wide) in paragraph at lines 96--96
 $[]$ 
 []

File: figures/IntroTrigGraphics/TheUnitCircle-9.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-9.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-10.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-10.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 96--96
[][]
 []


Overfull \hbox (5.00003pt too wide) in paragraph at lines 96--96
 $[]$ 
 []


Underfull \vbox (badness 3668) has occurred while \output is active []

 [319]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 107--108
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 107--108

 []

[320]
File: figures/IntroTrigGraphics/TheUnitCircle-11.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-11.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-12.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-12.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 168--169
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 168--169

 []

File: figures/IntroTrigGraphics/TheUnitCircle-13.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-13.pdf" >
Underfull \hbox (badness 1895) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.35: |Reference angle $[]$ for a
 []

File: figures/IntroTrigGraphics/TheUnitCircle-14.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-14.pdf" >
Underfull \hbox (badness 1895) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.36: |Reference angle $[]$ for a
 []

File: figures/IntroTrigGraphics/TheUnitCircle-15.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-15.pdf" >
Underfull \hbox (badness 1895) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.37: |Reference angle $[]$ for a
 []

File: figures/IntroTrigGraphics/TheUnitCircle-16.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-16.pdf" >
Underfull \hbox (badness 1895) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.38: |Reference angle $[]$ for a
 []

[321]
File: figures/IntroTrigGraphics/TheUnitCircle-17.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-17.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.39: |Finding $[] []$ and
 []

File: figures/IntroTrigGraphics/TheUnitCircle-18.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-18.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.40: |Finding $[] []$ and
 []

File: figures/IntroTrigGraphics/TheUnitCircle-19.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-19.pdf" >
Underfull \hbox (badness 7273) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.41: |Finding $[] []$ and
 []

File: figures/IntroTrigGraphics/TheUnitCircle-20.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-20.pdf" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.42: |Finding $[] []$ and
 []

[322]
File: figures/IntroTrigGraphics/TheUnitCircle-21.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-21.pdf" >
Overfull \hbox (132.9989pt too wide) in paragraph at lines 253--254
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [323]
File: figures/IntroTrigGraphics/TheUnitCircle-23.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-23.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-24.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-24.pdf" >
Overfull \hbox (27.00003pt too wide) in paragraph at lines 369--369
 $[]$ 
 []

File: figures/IntroTrigGraphics/TheUnitCircle-25.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-25.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-26.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-26.pdf" >
Overfull \hbox (27.00003pt too wide) in paragraph at lines 369--369
 $[]$ 
 []

File: figures/IntroTrigGraphics/TheUnitCircle-22.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-22.pdf" > [324]
File: figures/IntroTrigGraphics/TheUnitCircle-27.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-27.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-28.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-28.pdf" >
Overfull \hbox (27.00003pt too wide) in paragraph at lines 369--369
 $[]$ 
 []

File: figures/IntroTrigGraphics/TheUnitCircle-29.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-29.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-30.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-30.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 369--369
[][]
 []


Overfull \hbox (27.00003pt too wide) in paragraph at lines 369--369
 $[]$ 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [325]
File: figures/IntroTrigGraphics/TheUnitCircle-31.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-31.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-32.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-32.pdf" >
Overfull \hbox (15.00003pt too wide) in paragraph at lines 452--452
 $[]$ 
 []

[326]
File: figures/IntroTrigGraphics/TheUnitCircle-33.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-33.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-34.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-34.pdf" >
Overfull \hbox (15.00003pt too wide) in paragraph at lines 452--452
 $[]$ 
 []

File: figures/IntroTrigGraphics/TheUnitCircle-35.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-35.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-36.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-36.pdf" >
Overfull \hbox (15.00003pt too wide) in paragraph at lines 452--452
 $[]$ 
 []

[327]
File: figures/IntroTrigGraphics/TheUnitCircle-37.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-37.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-38.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-38.pdf" >
Overfull \hbox (7.99901pt too wide) in paragraph at lines 467--472
[][]
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 488--489
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 488--489

 []

[328]
Underfull \hbox (badness 10000) in paragraph at lines 519--519

 []


Underfull \vbox (badness 3514) has occurred while \output is active []

File: figures/IntroTrigGraphics/TheUnitCircle-39.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-39.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-40.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-40.pdf" >
Underfull \hbox (badness 1783) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 8.54: |A point on the Earth at
 []

[329]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 529--530
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 529--530

 []

File: figures/IntroTrigGraphics/TheUnitCircle-41.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TheUnitCircle-41.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 563--564
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 563--564

 []


Underfull \vbox (badness 7273) has occurred while \output is active []

File: figures/IntroTrigGraphics/TheUnitCircle-42.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-42.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-43.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-43.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[330]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 609--610
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 609--610

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/IntroTrigGraphics/TheUnitCircle-44.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-44.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-45.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-45.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-46.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-46.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-47.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-47.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[331] [332]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [333

]
File: figures/IntroTrigGraphics/TheUnitCircle-48.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TheUnitCircle-48.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-49.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-49.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-50.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-50.pdf" >
File: figures/IntroTrigGraphics/TheUnitCircle-48.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TheUnitCircle-48.pdf" > [334] [335])
(text_pre/07_CircularFunctions.tex
Overfull \hbox (0.72336pt too wide) in paragraph at lines 1--1
[]\EU1/Calibri(0)/bx/n/14.4 The Six Circular Functions and Fundamental Iden-
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 30--31
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 30--31

 []

File: figures/IntroTrigGraphics/CircularFunctions-1.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/CircularFunctions-1.pdf" > [336

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 61--62
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 61--62

 []


Overfull \hbox (5.3962pt too wide) in paragraph at lines 98--98
[]\EU1/Calibri(0)/m/n/10 According to Theorem []55[], $[] [] \OT1/cmr/m/n/10 = 
[]$\EU1/Calibri(0)/m/n/10 . Hence, $[] [] \OT1/cmr/m/n/10 = [] =
 []


Overfull \hbox (6.23792pt too wide) in paragraph at lines 98--98
[][]\OT1/cmr/m/n/10 ([]) = []$\EU1/Calibri(0)/m/n/10 , to find $[]\OT1/cmr/m/n/
10 ([])$ \EU1/Calibri(0)/m/n/10 by knowing $[]\OT1/cmr/m/n/10 ([])$\EU1/Calibri
(0)/m/n/10 . Substituting, we get $[][]\OT1/cmr/m/n/10 ([]) +
 []

[337]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 132--133
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 132--133

 []


Underfull \vbox (badness 1048) has occurred while \output is active []


Underfull \hbox (badness 1708) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 As we shall see shortly, when solving
 []

[338]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 229--230
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 229--230

 []


Underfull \vbox (badness 2368) has occurred while \output is active []

File: figures/IntroTrigGraphics/CircularFunctions-2.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-2.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-3.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-3.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/IntroTrigGraphics/CircularFunctions-4.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/CircularFunctions-4.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-5.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-5.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[339]
Underfull \hbox (badness 6284) in paragraph at lines 335--335
[]$\OT1/cmr/m/n/10 ([]([]) \OMS/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 ([]))([]([]) 
+
 []


Overfull \hbox (0.4019pt too wide) in paragraph at lines 335--335
[]$[] []\OT1/cmr/m/n/10 ([]) []([]) = [] \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (4.07538pt too wide) in paragraph at lines 335--335
[]\EU1/Calibri(0)/m/n/10 Starting with the right hand side of $[]\OT1/cmr/m/n/1
0 ([]) = []([]) []([])$\EU1/Calibri(0)/m/n/10 , we use $[]\OT1/cmr/m/n/10 ([]) 
=
 []

[340]
Overfull \hbox (11.86598pt too wide) in paragraph at lines 335--335
[]\EU1/Calibri(0)/m/n/10 Expanding the left hand side of the equation gives: $\
OT1/cmr/m/n/10 ([]([]) \OMS/cmsy/m/n/10 ^^@ []\OT1/cmr/m/n/10 ([]))([]([]) +
 []


Overfull \hbox (4.26395pt too wide) in paragraph at lines 335--335
[]\OT1/cmr/m/n/10 ([])) = [][]([]) \OMS/cmsy/m/n/10 ^^@ [][]\OT1/cmr/m/n/10 ([]
)$\EU1/Calibri(0)/m/n/10 . According to Theorem []57[], $[][]\OT1/cmr/m/n/10 ([
]) \OMS/cmsy/m/n/10 ^^@ [][]\OT1/cmr/m/n/10 ([]) =
 []


Overfull \hbox (40.79053pt too wide) detected at line 335
[]
 []


Overfull \hbox (56.89603pt too wide) detected at line 335
[]
 []


Overfull \hbox (11.47684pt too wide) detected at line 335
[]
 []

[341]
Overfull \hbox (21.27893pt too wide) detected at line 335
[]
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 360--361
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 360--361

 []

[342]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 387--388
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 387--388

 []

[343]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 411--412
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 411--412

 []


Underfull \hbox (badness 10000) in paragraph at lines 434--434

 []


Underfull \vbox (badness 1005) has occurred while \output is active []

 [344]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 445--446
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 445--446

 []


Underfull \hbox (badness 10000) in paragraph at lines 497--497

 []


Overfull \hbox (11.83702pt too wide) in paragraph at lines 497--497
[]\EU1/Calibri(0)/m/n/10 Using Theorem []59[], we get a pair of equations: $[] 
[] \OT1/cmr/m/n/10 = []$ \EU1/Calibri(0)/m/n/10 and $[] [] \OT1/cmr/m/n/10 =
 []


Underfull \vbox (badness 1365) has occurred while \output is active []

File: figures/IntroTrigGraphics/CircularFunctions-6.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-6.pdf" >
Overfull \hbox (16.99959pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/IntroTrigGraphics/CircularFunctions-7.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/CircularFunctions-7.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-8.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-8.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-9.pdf Graphic file (type QTm)


<use  "figures/IntroTrigGraphics/CircularFunctions-9.pdf" > [345]
File: figures/IntroTrigGraphics/CircularFunctions-10.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-10.pdf" >
Underfull \vbox (badness 1337) has occurred while \output is active []

 [346]
Overfull \hbox (31.39998pt too wide) in paragraph at lines 573--574
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 573--574

 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 2529) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Notice we have used the variable ‘$[]$’
 []

[347] [348]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [349

]
File: figures/IntroTrigGraphics/CircularFunctions-11.pdf Graphic file (type QTm
)
 <use  "figures/IntroTrigGraphics/CircularFunctions-11.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-12.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-12.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-13.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-13.pdf" >
File: figures/IntroTrigGraphics/CircularFunctions-14.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-14.pdf" > [350]
File: figures/IntroTrigGraphics/CircularFunctions-15.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-15.pdf" > [351] [352]
File: figures/IntroTrigGraphics/CircularFunctions-16.pdf Graphic file (type QTm
)

<use  "figures/IntroTrigGraphics/CircularFunctions-16.pdf" > [353])
(text_pre/07_Identities.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 32--33
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 32--33

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 59--60
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 59--60

 []

File: figures/IntroTrigGraphics/Identities-1.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Identities-1.pdf" >
File: figures/IntroTrigGraphics/Identities-2.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Identities-2.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[354

]
Overfull \hbox (1.71594pt too wide) in paragraph at lines 89--89
[] 
 []


Overfull \hbox (1.53867pt too wide) in paragraph at lines 104--104
[] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 159--159

 []

File: figures/IntroTrigGraphics/Identities-3.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/Identities-3.pdf" >
File: figures/IntroTrigGraphics/Identities-4.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Identities-4.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []


Underfull \hbox (badness 1552) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 In Figure []8.68[], the $[]$angles $[][][]$ and
 []

[355]
Overfull \hbox (9.06137pt too wide) in paragraph at lines 168--169
[]\EU1/Calibri(0)/m/n/10 which says, in words, that the ‘co’sine of an angle is
 the sine of its ‘co’mplement.
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 193--194
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 193--194

 []

[356]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 220--221
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 220--221

 []


Underfull \hbox (badness 10000) in paragraph at lines 279--279

 []

[357]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 298--299
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 298--299

 []

[358]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 319--320
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 319--320

 []


Overfull \hbox (8.8624pt too wide) in paragraph at lines 323--324
\EU1/Calibri(0)/m/n/10 change’ squares of cosine and sine via the Pythagorean I
dentity $[][]\OT1/cmr/m/n/10 ([]) + [][]([]) =
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [359]
Underfull \hbox (badness 10000) in paragraph at lines 389--389

 []


Overfull \hbox (1.68065pt too wide) in paragraph at lines 389--389
[]\EU1/Calibri(0)/m/n/10 We start with the right hand side of the identity and 
note that $[] \OT1/cmr/m/n/10 + [][]([]) =
 []


Overfull \hbox (13.01225pt too wide) detected at line 389
[]
 []

[360]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 406--407
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 406--407

 []

[361]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 454--455
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 454--455

 []


Underfull \hbox (badness 10000) in paragraph at lines 510--510

 []

[362] [363]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 531--532
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 531--532

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 550--551
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 550--551

 []


Underfull \hbox (badness 10000) in paragraph at lines 583--583

 []


Overfull \hbox (12.458pt too wide) in paragraph at lines 583--583
\EU1/Calibri(0)/m/n/10 where the last equality is courtesy of the even identity
 for cosine, $[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@[][]\OT1/cmr/m/n/10 ) =
 []


Underfull \hbox (badness 1442) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The identities in Theorem []69[] are also
 []

[364] [365]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


Underfull \hbox (badness 10000) in paragraph at lines 591--591
[]$[] \OT1/cmr/m/n/9 = []([]) [] +
 []

[366

]
Underfull \hbox (badness 10000) in paragraph at lines 591--591
[]$[] \OT1/cmr/m/n/9 = []([]) [] \OMS/cmsy/m/n/9 ^^@
 []

[367] [368]) (text_pre/07_TrigGraphs.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 14--15
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 14--15

 []


Underfull \hbox (badness 10000) in paragraph at lines 50--50
[]\EU1/Calibri(0)/m/n/10 is continuous and
 []


Underfull \hbox (badness 10000) in paragraph at lines 50--50
[]\EU1/Calibri(0)/m/n/10 is continuous and
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 50--51
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 50--51

 []

[369

]
File: figures/IntroTrigGraphics/TrigGraphs-2.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-2.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-4.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-4.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-1.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-1.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/IntroTrigGraphics/TrigGraphs-3.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-3.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[370]
File: figures/IntroTrigGraphics/TrigGraphs-5.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-5.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 277--277
 [] 
 []

File: figures/IntroTrigGraphics/TrigGraphs-6.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-6.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 277--277
 [] 
 []

[371]
Overfull \hbox (2.36513pt too wide) in paragraph at lines 277--277
[]\EU1/Calibri(0)/m/n/10 One cycle was graphed on the interval $[]$ so the peri
od is $[] \OMS/cmsy/m/n/10 ^^@ [] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 308--309
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 308--309

 []

File: figures/IntroTrigGraphics/TrigGraphs-7.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-7.pdf" > [372]
Underfull \vbox (badness 10000) has occurred while \output is active []

 [373]
File: figures/IntroTrigGraphics/TrigGraphs-9.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-9.pdf" >
Overfull \hbox (15.00003pt too wide) in paragraph at lines 361--361
 $[]$ 
 []

File: figures/IntroTrigGraphics/TrigGraphs-8.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-8.pdf" > [374]
Overfull \hbox (1.84683pt too wide) in paragraph at lines 403--403
\EU1/Calibri(0)/m/n/10 mulas and match up corresponding coefficients. Equating 
$[]\OT1/cmr/m/n/10 ([]) = []([][]) \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (0.32655pt too wide) in paragraph at lines 403--403
[] []\OT1/cmr/m/n/10 ([]) = []$\EU1/Calibri(0)/m/n/10 , or $[]\OT1/cmr/m/n/10 (
[]) = []$\EU1/Calibri(0)/m/n/10 , and $[] []\OT1/cmr/m/n/10 ([]) = \OMS/cmsy/m/
n/10 ^^@[]$\EU1/Calibri(0)/m/n/10 , which means $[]\OT1/cmr/m/n/10 ([]) =
 []

[375]
File: figures/IntroTrigGraphics/TrigGraphs-10.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-10.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 419--438
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [376]
File: figures/IntroTrigGraphics/TrigGraphs-11.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-11.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-12.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-12.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 465--484
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [377]
File: figures/IntroTrigGraphics/TrigGraphs-13.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-13.pdf" >
Overfull \hbox (31.39998pt too wide) in paragraph at lines 555--556
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 555--556

 []


Overfull \hbox (61.50717pt too wide) in paragraph at lines 515--558
 $[]$ 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [378]
File: figures/IntroTrigGraphics/TrigGraphs-14.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-14.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 676--676
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [379]
Overfull \hbox (8.0763pt too wide) in paragraph at lines 676--676
[]\EU1/Calibri(0)/m/n/10 Proceeding as before, we set the argument of cosecant 
in $[]\OT1/cmr/m/n/10 ([]) = []$
 []

File: figures/IntroTrigGraphics/TrigGraphs-15.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-15.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 676--676
 [] 
 []

[380]
File: figures/IntroTrigGraphics/TrigGraphs-16.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-16.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 690--710
 [] 
 []

File: figures/IntroTrigGraphics/TrigGraphs-17.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigGraphs-17.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-18.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-18.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 741--761
 [] 
 []

[381]
File: figures/IntroTrigGraphics/TrigGraphs-19.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-19.pdf" >
Overfull \hbox (31.39998pt too wide) in paragraph at lines 829--830
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 829--830

 []


Overfull \hbox (61.50717pt too wide) in paragraph at lines 789--832
 $[]$ 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [382]
File: figures/IntroTrigGraphics/TrigGraphs-20.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-20.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 955--955
 [] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [383]
File: figures/IntroTrigGraphics/TrigGraphs-21.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-21.pdf" >
Overfull \hbox (24.0pt too wide) in paragraph at lines 955--955
 [] 
 []

[384]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [385

] [386])
Chapter 9.
(text_pre/07_ArcTrig.tex
File: figures/IntroTrigGraphics/ArcTrig-1.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/ArcTrig-1.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-4.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-4.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 93--94
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 93--94

 []

File: figures/IntroTrigGraphics/ArcTrig-2.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-2.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-3.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-3.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[387




]
Underfull \hbox (badness 10000) in paragraph at lines 189--189

 []


Overfull \hbox (4.0164pt too wide) in paragraph at lines 189--189
[]\EU1/Calibri(0)/m/n/10 The number $[] \OT1/cmr/m/n/10 = [] []$ \EU1/Calibri(0
)/m/n/10 lies in the interval $\OT1/cmr/m/n/10 [[]\OML/cmm/m/it/10 ; []\OT1/cmr
/m/n/10 ]$ \EU1/Calibri(0)/m/n/10 with $[]\OT1/cmr/m/n/10 ([]) =
 []

File: figures/IntroTrigGraphics/ArcTrig-5.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-5.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-6.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-6.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[388]
Overfull \hbox (6.73148pt too wide) in paragraph at lines 189--189
\EU1/Calibri(0)/m/n/10 consider our substitution $[] \OT1/cmr/m/n/10 = []([])$\
EU1/Calibri(0)/m/n/10 . Since the domain of $[]\OT1/cmr/m/n/10 ([])$
 []


Underfull \hbox (badness 1184) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 is to use the identity $[] \OT1/cmr/m/n/9 + [][]([]) =
 []

[389]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 263--264
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 263--264

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/IntroTrigGraphics/ArcTrig-7.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-7.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-8.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-8.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[390]
Underfull \hbox (badness 10000) in paragraph at lines 356--356

 []


Overfull \hbox (0.1629pt too wide) in paragraph at lines 356--356
\EU1/Calibri(0)/m/n/10 we have that $[]$ belongs to the interval $\OT1/cmr/m/n/
10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )$ \EU1/Calibri(0)/m/n/10 and $[]\OT
1/cmr/m/n/10 ([]) = \OMS/cmsy/m/n/10 ^^@[]$\EU1/Calibri(0)/m/n/10 . Hence,
 []

File: figures/IntroTrigGraphics/ArcTrig-9.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-9.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-10.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-10.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[391]
Underfull \hbox (badness 1924) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 It’s always a good idea to make sure
 []


Underfull \hbox (badness 1297) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 Check our work back in Example []162[].
 []

[392]
File: figures/IntroTrigGraphics/ArcTrig-11.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/ArcTrig-11.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-12.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-12.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 440--441
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 440--441

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [393]
Underfull \hbox (badness 10000) in paragraph at lines 542--542

 []


Overfull \hbox (18.16574pt too wide) in paragraph at lines 542--542
\EU1/Calibri(0)/m/n/10 by working ‘inside out’ which yields $[] [] \OT1/cmr/m/n
/10 = [](\OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 ) =
 []


Overfull \hbox (5.75223pt too wide) in paragraph at lines 542--542
[]\EU1/Calibri(0)/m/n/10 One way to begin to simplify $[] []$ is to let $[] \OT
1/cmr/m/n/10 = [](\OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 )$\EU1/Calibri(0)/m/n/1
0 .
 []

File: figures/IntroTrigGraphics/ArcTrig-13.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-13.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-14.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-14.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-15.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-15.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-16.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-16.pdf" > [394]
Overfull \hbox (3.72256pt too wide) in paragraph at lines 542--542
\EU1/Calibri(0)/m/n/10 had no additional restrictions on $[]$, the equivalence 
$[]\OT1/cmr/m/n/10 ([]([][])) =
 []

[395]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 603--604
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 603--604

 []


Underfull \hbox (badness 10000) in paragraph at lines 715--715

 []

File: figures/IntroTrigGraphics/ArcTrig-17.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-17.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-18.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-18.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-19.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-19.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-20.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-20.pdf" > [396]
Overfull \hbox (1.70035pt too wide) in paragraph at lines 715--715
[]\EU1/Calibri(0)/m/n/10 Since $[] \OMS/cmsy/m/n/10 ^^U []$\EU1/Calibri(0)/m/n/
10 , we can use Theorem []78[] to get $[]\OT1/cmr/m/n/10 ([]) = [] [] =
 []


Overfull \hbox (20.47762pt too wide) in paragraph at lines 715--715
[]$ \EU1/Calibri(0)/m/n/10 holds for all $[]$ in the domain of $[] \OT1/cmr/m/n
/10 = []([])$\EU1/Calibri(0)/m/n/10 , namely $\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10
 ^^@1\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 ] \OMS/cmsy/m/n/1
0 [
 []

[397]
Underfull \hbox (badness 10000) in paragraph at lines 832--832

 []


Overfull \hbox (2.84845pt too wide) in paragraph at lines 832--832
[]\EU1/Calibri(0)/m/n/10 Use a calculator to approximate the following values t
o four decimal places. 
 []

[398]
Overfull \hbox (25.11682pt too wide) in paragraph at lines 832--832
[]\OT1/cmr/m/n/10 ([])$ \EU1/Calibri(0)/m/n/10 as $[]\OT1/cmr/m/n/10 ([]) = [] 
[]$\EU1/Calibri(0)/m/n/10 . In ‘radian’ mode, we find $[]\OT1/cmr/m/n/10 ([]) =

 []

File: figures/IntroTrigGraphics/ArcTrig-21.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-21.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-22.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-22.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-23.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-23.pdf" >
File: figures/IntroTrigGraphics/ArcTrig1.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig1.png" > [399]
Underfull \vbox (badness 1009) has occurred while \output is active []

File: figures/IntroTrigGraphics/ArcTrig2.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig2.png" >
File: figures/IntroTrigGraphics/ArcTrig3.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig3.png" >
Requested font "[lmmono9-regular]" at 9.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/opentype/public/lm/lmmono9-regular.otf

Underfull \hbox (badness 1092) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 defined function in GeoGebra, we use
 []


Underfull \hbox (badness 10000) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 the syntax \EU1/lmtt/m/n/9 Function[<function>,
 []

[400]
File: figures/IntroTrigGraphics/ArcTrig05.jpg Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/ArcTrig05.jpg" >
File: figures/IntroTrigGraphics/ArcTrig06.jpg Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig06.jpg" >
Underfull \hbox (badness 10000) in paragraph at lines 861--861

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/IntroTrigGraphics/ArcTrig-24.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-24.pdf" > [401]
File: figures/IntroTrigGraphics/ArcTrig-25.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-25.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-26.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-26.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/IntroTrigGraphics/ArcTrig-27.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/ArcTrig-27.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-28.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-28.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[402]
File: figures/IntroTrigGraphics/ArcTrig-29.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/ArcTrig-29.pdf" >
File: figures/IntroTrigGraphics/ArcTrig-30.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-30.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[403]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [404

] [405] [406] [407] [408]
File: figures/IntroTrigGraphics/ArcTrig-31.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/ArcTrig-31.pdf" > [409])
(text_pre/07_TrigEquIneq.tex
Underfull \hbox (badness 4699) in paragraph at lines 23--23
[][][][]\EU1/Calibri(0)/bx/n/10 Key Idea 39 Strategies for Solving Basic Equati
ons Involving
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 23--24
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 23--24

 []

[410

]
File: figures/IntroTrigGraphics/TrigEquIneq01.png Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigEquIneq01.png" >
File: figures/IntroTrigGraphics/TrigEquIneq02.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq02.png" > [411]
File: figures/IntroTrigGraphics/TrigEquIneq03.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq03.png" >
Underfull \hbox (badness 1077) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 graphing calculator. On many calcula-
 []

File: figures/IntroTrigGraphics/TrigEquIneq04.png Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq04.png" > [412]
File: figures/IntroTrigGraphics/TrigEquIneq05.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq05.png" > [413]
Overfull \hbox (5.08246pt too wide) in paragraph at lines 280--280
\EU1/Calibri(0)/m/n/10 Solve the following equations and list the solutions whi
ch lie in the interval $\OT1/cmr/m/n/10 [[]\OML/cmm/m/it/10 ; [][]\OT1/cmr/m/n/
10 )$\EU1/Calibri(0)/m/n/10 .
 []

File: figures/IntroTrigGraphics/TrigEquIneq06.png Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq06.png" >
File: figures/IntroTrigGraphics/TrigEquIneq07.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq07.png" >
File: figures/IntroTrigGraphics/TrigEquIneq08.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq08.png" > [414]
File: figures/IntroTrigGraphics/TrigEquIneq09.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq09.png" >
File: figures/IntroTrigGraphics/TrigEquIneq10.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq10.png" > [415]
Overfull \hbox (4.62445pt too wide) in paragraph at lines 280--280
\EU1/Calibri(0)/m/n/10 Hence, the equation $[]\OT1/cmr/m/n/10 ([][]) = []([][])
$ \EU1/Calibri(0)/m/n/10 is equivalent to $\OMS/cmsy/m/n/10 ^^@[] []\OT1/cmr/m/
n/10 ([][]) []([]) =
 []


Overfull \hbox (4.0654pt too wide) in paragraph at lines 280--280
\EU1/Calibri(0)/m/n/10 cular functions or their arguments to match in the equat
ion $[]\OT1/cmr/m/n/10 ([]) [] [] +
 []

File: figures/IntroTrigGraphics/TrigEquIneq11.png Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq11.png" >
File: figures/IntroTrigGraphics/TrigEquIneq12.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq12.png" >
File: figures/IntroTrigGraphics/TrigEquIneq13.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq13.png" >
File: figures/IntroTrigGraphics/TrigEquIneq14.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq14.png" >
Underfull \hbox (badness 5374) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.35: |Solving $[]\OT1/cmr/m/n/9 ([]) []([]) +
 []

[416]
Overfull \hbox (0.80087pt too wide) in paragraph at lines 284--285
[]\EU1/Calibri(0)/m/n/10 Unfortunately there is no systematic approach to solvi
ng trigonometric equa-
 []

File: figures/IntroTrigGraphics/TrigEquIneq15.png Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq15.png" >
Underfull \hbox (badness 1215) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 See page []148[], Example []67[], page []202[],
 []

File: figures/IntroTrigGraphics/TrigEquIneq_new-1.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq_new-1.pdf" >
File: figures/IntroTrigGraphics/TrigEquIneq16.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq16.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[417]
File: figures/IntroTrigGraphics/TrigEquIneq_new-2.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigEquIneq_new-2.pdf" >
File: figures/IntroTrigGraphics/TrigEquIneq17.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq17.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/IntroTrigGraphics/TrigEquIneq_new-3.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq_new-3.pdf" >
File: figures/IntroTrigGraphics/TrigEquIneq18.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq18.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[418]
Overfull \hbox (2.70845pt too wide) in paragraph at lines 417--417
\EU1/Calibri(0)/m/n/10 only concern comes from zeros in the denominator. Solvin
g $[] [] \OT1/cmr/m/n/10 =
 []

File: figures/IntroTrigGraphics/TrigEquIneq_new-4.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq_new-4.pdf" >
Overfull \hbox (4.56561pt too wide) in paragraph at lines 417--417
\EU1/Calibri(0)/m/n/10 We can check our answer by substituting in values of $[]
$ to see that it matches
 []


Overfull \hbox (37.68733pt too wide) in paragraph at lines 417--417
\EU1/Calibri(0)/m/n/10 builder notation, the domain is $[]$,
 []

File: figures/IntroTrigGraphics/TrigEquIneq_new-5.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq_new-5.pdf" >
Overfull \hbox (34.62463pt too wide) detected at line 417
[] [] \OMS/cmsy/m/n/10 [ [] [ [] [ [] [ [] [ [] [ [] [ []
 []

[419]
File: figures/IntroTrigGraphics/TrigEquIneq_new-6.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigEquIneq_new-6.pdf" > [420]
File: figures/IntroTrigGraphics/TrigEquIneq19.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq19.png" >
File: figures/IntroTrigGraphics/TrigEquIneq20.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq20.png" > [421]
Overfull \hbox (1.47473pt too wide) in paragraph at lines 527--527
[]\EU1/Calibri(0)/m/n/10 Since the inverse trigonometric functions are continuo
us on their domains,
 []

File: figures/IntroTrigGraphics/TrigEquIneq21.png Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq21.png" >
File: figures/IntroTrigGraphics/TrigEquIneq22.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq22.png" >
Underfull \hbox (badness 10000) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.43: |Solving $[] [][]\OT1/cmr/m/n/9 ([]) \OMS/
cmsy/m/n/9 ^^@
 []

File: figures/IntroTrigGraphics/TrigEquIneq_new-7.pdf Graphic file (type QTm)
<use  "figures/IntroTrigGraphics/TrigEquIneq_new-7.pdf" >
File: figures/IntroTrigGraphics/TrigEquIneq23.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq23.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[422]
File: figures/IntroTrigGraphics/TrigEquIneq_new-8.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigEquIneq_new-8.pdf" >
File: figures/IntroTrigGraphics/TrigEquIneq24.png Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigEquIneq24.png" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][] 
 []

[423]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [424

] [425] [426]) (text_pre/08_Sinusoid.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 23--24
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 23--24

 []

File: figures/AppExtGraphics/Sinusoid-1.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/Sinusoid-1.pdf" >
File: figures/AppExtGraphics/Sinusoid-2.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid-2.pdf" > [427

]
File: figures/AppExtGraphics/Sinusoid-3.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid-3.pdf" > [428]
File: figures/AppExtGraphics/Sinusoid-5.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid-5.pdf" >
File: figures/AppExtGraphics/Sinusoid-6.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid-6.pdf" >
File: figures/AppExtGraphics/Sinusoid-7.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid-7.pdf" >
Overfull \hbox (4.00293pt too wide) in paragraph at lines 157--168
 [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 190--191
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 190--191

 []


Underfull \vbox (badness 10000) has occurred while \output is active []


Underfull \hbox (badness 1831) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 The sign conventions here are carried
 []

[429] [430]
Underfull \hbox (badness 10000) in paragraph at lines 317--317

 []


Overfull \hbox (9.93489pt too wide) in paragraph at lines 317--317
[]\EU1/Calibri(0)/m/n/10 Write $[]\OT1/cmr/m/n/10 ([]) = [][][] []([]) + [][][]
[] []([])$ \EU1/Calibri(0)/m/n/10 in the form $[]\OT1/cmr/m/n/10 ([]) = []([]) 
[]([][] +
 []


Overfull \hbox (2.72087pt too wide) in paragraph at lines 317--317
\EU1/Calibri(0)/m/n/10 introduced in Exercise []36[] from Section []8.5[]. We f
ind $[] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (5.35478pt too wide) in paragraph at lines 317--317
\EU1/Calibri(0)/m/n/10 zero. Indeed, if we graph $[] \OT1/cmr/m/n/10 = \OMS/cms
y/m/n/10 ^^F[][][][]$ \EU1/Calibri(0)/m/n/10 along with $[] \OT1/cmr/m/n/10 = [
][][][] [] []$
 []

File: figures/AppExtGraphics/Sinusoid-8.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/Sinusoid-8.pdf" >
File: figures/AppExtGraphics/Sinusoid01.png Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid01.png" >
File: figures/AppExtGraphics/Sinusoid02.png Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid02.png" >
File: figures/AppExtGraphics/Sinusoid03.png Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid03.png" >
Overfull \hbox (17.12872pt too wide) has occurred while \output is active
 [][][] 
 []

[431]
File: figures/AppExtGraphics/Sinusoid04.png Graphic file (type QTm)
 <use  "figures/AppExtGraphics/Sinusoid04.png" >
File: figures/AppExtGraphics/Sinusoid05.png Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid05.png" >
Overfull \hbox (22.79163pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/AppExtGraphics/Sinusoid06.png Graphic file (type QTm)
<use  "figures/AppExtGraphics/Sinusoid06.png" >
File: figures/AppExtGraphics/Sinusoid07.png Graphic file (type QTm)

<use  "figures/AppExtGraphics/Sinusoid07.png" >
Overfull \hbox (5.28072pt too wide) has occurred while \output is active
 [][][] 
 []

[432]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/AppExtGraphics/Sinusoid-9.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/Sinusoid-9.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 319--319
[]\EU1/Calibri(0)/m/n/9 With the help of your classmates, research
 []

[433

]) (text_pre/08_LawofSines.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 30--31
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 30--31

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/AppExtGraphics/LawofSines-1.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-1.pdf" > [434

]
File: figures/AppExtGraphics/LawofSines-2.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-2.pdf" >
File: figures/AppExtGraphics/LawofSines-3.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-3.pdf" >
File: figures/AppExtGraphics/LawofSines-4.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-4.pdf" >
Overfull \hbox (4.00293pt too wide) in paragraph at lines 40--45
 [] 
 []

File: figures/AppExtGraphics/LawofSines-5.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofSines-5.pdf" >
File: figures/AppExtGraphics/LawofSines-6.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-6.pdf" >
File: figures/AppExtGraphics/LawofSines-7.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-7.pdf" > [435]
File: figures/AppExtGraphics/LawofSines-8.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-8.pdf" >
Underfull \hbox (badness 1270) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.59: |Triangle for Example []178[]
 []

File: figures/AppExtGraphics/LawofSines-9.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofSines-9.pdf" >
Underfull \hbox (badness 1270) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.60: |Triangle for Example []178[]
 []

[436]
File: figures/AppExtGraphics/LawofSines-12.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/LawofSines-12.pdf" >
File: figures/AppExtGraphics/LawofSines-13.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-13.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 155--155
$[]$ 
 []

File: figures/AppExtGraphics/LawofSines-10.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofSines-10.pdf" >
Underfull \hbox (badness 1270) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.62: |Triangle for Example []178[]
 []

File: figures/AppExtGraphics/LawofSines-11.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofSines-11.pdf" >
Underfull \hbox (badness 1270) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.63: |Triangle for Example []178[]
 []

[437]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 178--179
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 178--179

 []

File: figures/AppExtGraphics/LawofSines-15.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofSines-15.pdf" >
File: figures/AppExtGraphics/LawofSines-16.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-16.pdf" >
Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/AppExtGraphics/LawofSines-14.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-14.pdf" >
Underfull \hbox (badness 1270) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.65: |Triangle for Example []178[]
 []

[438]
File: figures/AppExtGraphics/LawofSines-17.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/LawofSines-17.pdf" >
File: figures/AppExtGraphics/LawofSines-18.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-18.pdf" >
File: figures/AppExtGraphics/LawofSines-19.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-19.pdf" >
File: figures/AppExtGraphics/LawofSines-20.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofSines-20.pdf" >
Overfull \hbox (4.49954pt too wide) has occurred while \output is active
 [][][] 
 []

[439]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 243--244
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 243--244

 []

[440]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [441

]
File: figures/AppExtGraphics/LawofSines-21.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/LawofSines-21.pdf" > [442])
(text_pre/08_LawofCosines.tex
Overfull \hbox (31.39998pt too wide) in paragraph at lines 18--19
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 18--19

 []


Overfull \hbox (40.0pt too wide) in paragraph at lines 10--22
$[]$ 
 []

File: figures/AppExtGraphics/LawofCosines-1.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofCosines-1.pdf" >
Overfull \hbox (15.0pt too wide) in paragraph at lines 29--37
[]$[]$ 
 []

[443

] [444]
Overfull \hbox (16.11868pt too wide) in paragraph at lines 99--99
\EU1/Calibri(0)/m/n/10 this case using $[]\OT1/cmr/m/n/10 ([]) = []$\EU1/Calibr
i(0)/m/n/10 . Plugging in $[] \OT1/cmr/m/n/10 = []$\EU1/Calibri(0)/m/n/10 , $[]
 \OT1/cmr/m/n/10 = []$
 []

File: figures/AppExtGraphics/LawofCosines-2.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofCosines-2.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 99--99
[]$[]$ 
 []

[445]
File: figures/AppExtGraphics/LawofCosines-3.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/LawofCosines-3.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 99--99
[]$[]$ 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 124--125
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 124--125

 []

File: figures/AppExtGraphics/LawofCosines-4.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/LawofCosines-4.pdf" > [446] [447] [448]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/AppExtGraphics/LawofCosines-5.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/LawofCosines-5.pdf" > [449

] [450])
(text_pre/08_IntroPolar.tex
File: figures/AppExtGraphics/IntroPolar-1.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-1.pdf" >
File: figures/AppExtGraphics/IntroPolar-2.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-2.pdf" >
Overfull \hbox (8.9991pt too wide) in paragraph at lines 13--17
 [] 
 []


Overfull \hbox (61.50717pt too wide) in paragraph at lines 10--22
 $[]$ 
 []

File: figures/AppExtGraphics/IntroPolar-3.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-3.pdf" >
File: figures/AppExtGraphics/IntroPolar-4.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-4.pdf" >
File: figures/AppExtGraphics/IntroPolar-5.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-5.pdf" >
Overfull \hbox (8.99913pt too wide) in paragraph at lines 33--38
 [] 
 []


Overfull \hbox (61.50717pt too wide) in paragraph at lines 30--43
 $[]$ 
 []

[451

]
File: figures/AppExtGraphics/IntroPolar-6.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-6.pdf" >
File: figures/AppExtGraphics/IntroPolar-7.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-7.pdf" >
File: figures/AppExtGraphics/IntroPolar-8.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-8.pdf" >
Overfull \hbox (29.99895pt too wide) in paragraph at lines 55--60
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-9.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-9.pdf" >
File: figures/AppExtGraphics/IntroPolar-10.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-10.pdf" >
File: figures/AppExtGraphics/IntroPolar-11.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-11.pdf" >
Overfull \hbox (31.99895pt too wide) in paragraph at lines 77--82
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-12.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-12.pdf" >
File: figures/AppExtGraphics/IntroPolar-13.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-13.pdf" >
File: figures/AppExtGraphics/IntroPolar-14.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-14.pdf" >
Overfull \hbox (34.999pt too wide) in paragraph at lines 100--105
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-15.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-15.pdf" >
File: figures/AppExtGraphics/IntroPolar-16.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-16.pdf" >
File: figures/AppExtGraphics/IntroPolar-17.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-17.pdf" >
Overfull \hbox (30.999pt too wide) in paragraph at lines 123--128
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-18.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-18.pdf" >
File: figures/AppExtGraphics/IntroPolar-19.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-19.pdf" >
File: figures/AppExtGraphics/IntroPolar-20.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-20.pdf" >
Overfull \hbox (40.999pt too wide) in paragraph at lines 146--151
 [] 
 []


Overfull \hbox (81.50717pt too wide) in paragraph at lines 143--156
 $[]$ 
 []

[452]
File: figures/AppExtGraphics/IntroPolar-21.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-21.pdf" >
File: figures/AppExtGraphics/IntroPolar-22.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-22.pdf" >
Overfull \hbox (66.5072pt too wide) in paragraph at lines 363--363
 $[]$ 
 []

File: figures/AppExtGraphics/IntroPolar-23.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-23.pdf" >
File: figures/AppExtGraphics/IntroPolar-24.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-24.pdf" >
Overfull \hbox (76.5072pt too wide) in paragraph at lines 363--363
 $[]$ 
 []

[453]
File: figures/AppExtGraphics/IntroPolar-25.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-25.pdf" >
File: figures/AppExtGraphics/IntroPolar-26.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-26.pdf" >
Overfull \hbox (7.999pt too wide) in paragraph at lines 363--363
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-27.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-27.pdf" >
File: figures/AppExtGraphics/IntroPolar-28.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-28.pdf" >
Overfull \hbox (8.99898pt too wide) in paragraph at lines 363--363
 [] 
 []

File: figures/AppExtGraphics/IntroPolar-29.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-29.pdf" >
File: figures/AppExtGraphics/IntroPolar-30.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-30.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 363--363
$[]$ 
 []

File: figures/AppExtGraphics/IntroPolar-31.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-31.pdf" >
File: figures/AppExtGraphics/IntroPolar-32.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-32.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 363--363
$[]$ 
 []

[454]
File: figures/AppExtGraphics/IntroPolar-33.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-33.pdf" >
File: figures/AppExtGraphics/IntroPolar-34.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-34.pdf" >
Overfull \hbox (13.99902pt too wide) in paragraph at lines 363--363
 [] 
 []


Overfull \hbox (116.5072pt too wide) in paragraph at lines 363--363
 $[]$ 
 []

File: figures/AppExtGraphics/IntroPolar-35.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-35.pdf" >
File: figures/AppExtGraphics/IntroPolar-36.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-36.pdf" >
Overfull \hbox (13.99902pt too wide) in paragraph at lines 363--363
 [] 
 []


Overfull \hbox (116.5072pt too wide) in paragraph at lines 363--363
 $[]$ 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 386--387
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 386--387

 []

[455]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 411--412
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 411--412

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [456]
Overfull \hbox (14.60414pt too wide) in paragraph at lines 458--458
\OT1/cmr/m/n/10 ([][]) [] = \OMS/cmsy/m/n/10 ^^@[]$ \EU1/Calibri(0)/m/n/10 and 
$[] \OT1/cmr/m/n/10 = [] []([]) = ([][]) [] [] = ([][]) [] =
 []

File: figures/AppExtGraphics/IntroPolar-37.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-37.pdf" >
Underfull \hbox (badness 1052) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.87: |$[]$ has rectangular coordi-
 []

File: figures/AppExtGraphics/IntroPolar-38.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-38.pdf" >
Underfull \hbox (badness 2261) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 nates $\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it
/9 ; \OMS/cmsy/m/n/9 ^^@[]\OT1/cmr/m/n/9 )$ \EU1/Calibri(0)/m/n/9 and polar coo
rdinates
 []

[457]
Overfull \hbox (5.72878pt too wide) in paragraph at lines 458--458
[]\EU1/Calibri(0)/m/n/10 The point $[]\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; \OM
S/cmsy/m/n/10 ^^@[]\OT1/cmr/m/n/10 )$ \EU1/Calibri(0)/m/n/10 lies along the neg
ative $[]$-axis. While we could go through
 []

File: figures/AppExtGraphics/IntroPolar-39.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-39.pdf" >
Underfull \hbox (badness 3557) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.89: |$[]$ has rectangular coor-
 []


Underfull \hbox (badness 2503) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 dinates $\OT1/cmr/m/n/9 ([]\OML/cmm/m/it/9 ; \OMS/cmsy/m/
n/9 ^^@[]\OT1/cmr/m/n/9 )$ \EU1/Calibri(0)/m/n/9 and polar coordinates
 []

File: figures/AppExtGraphics/IntroPolar-40.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/IntroPolar-40.pdf" >
Underfull \hbox (badness 4013) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 9.90: |$[]$ has rectangular coor-
 []


Underfull \hbox (badness 2503) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 dinates $\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/
it/9 ; []\OT1/cmr/m/n/9 )$ \EU1/Calibri(0)/m/n/9 and polar coordinates
 []

[458] [459]
Underfull \hbox (badness 2744) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 of a point are ‘equivalent’, we mean
 []


Underfull \hbox (badness 1072) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 that they represent the same point in
 []


Underfull \hbox (badness 1502) has occurred while \output is active
\OT1/cmr/m/n/9 (\OMS/cmsy/m/n/9 ^^@[]\OML/cmm/m/it/9 ; []\OT1/cmr/m/n/9 )$ \EU1
/Calibri(0)/m/n/9 are different, but when inter-
 []

[460] [461]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [462

] [463] [464]) (text_pre/08_PolarComplex.tex
File: figures/AppExtGraphics/PolarComplex-1.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/PolarComplex-1.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 36--37
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 36--37

 []


Underfull \hbox (badness 1092) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Saying that $[]\OT1/cmr/m/n/9 ([])$ \EU1/Calibri(0)/m/n
/9 and $[]\OT1/cmr/m/n/9 ([])$ \EU1/Calibri(0)/m/n/9 are ‘well-
 []

[465

] [466]
File: figures/AppExtGraphics/PolarComplex-2.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/PolarComplex-2.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 83--83
$[]$ 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 108--109
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 108--109

 []

[467]
Underfull \hbox (badness 10000) in paragraph at lines 177--177
[]\EU1/Calibri(0)/m/n/10 If $[]\OT1/cmr/m/n/10 ([]) = []$ \EU1/Calibri(0)/m/n/1
0 and $[]\OT1/cmr/m/n/10 ([]) \OML/cmm/m/it/10 > []$\EU1/Calibri(0)/m/n/10 , th
en $[]\OT1/cmr/m/n/10 ([]) =
 []


Underfull \hbox (badness 10000) in paragraph at lines 177--177
[]\EU1/Calibri(0)/m/n/10 If $[]\OT1/cmr/m/n/10 ([]) = []$ \EU1/Calibri(0)/m/n/1
0 and $[]\OT1/cmr/m/n/10 ([]) \OML/cmm/m/it/10 < []$\EU1/Calibri(0)/m/n/10 , th
en $[]\OT1/cmr/m/n/10 ([]) =
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 177--178
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 177--178

 []

[468]
File: figures/AppExtGraphics/PolarComplex-3.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/PolarComplex-3.pdf" >
Overfull \hbox (1.39998pt too wide) in paragraph at lines 207--208
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 207--208

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [469]
Underfull \hbox (badness 10000) in paragraph at lines 290--290

 []

[470]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 309--310
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 309--310

 []

[471] [472] [473]
File: figures/AppExtGraphics/PolarComplex-4.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/PolarComplex-4.pdf" >
File: figures/AppExtGraphics/PolarComplex-5.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/PolarComplex-5.pdf" >
Overfull \hbox (30.00092pt too wide) in paragraph at lines 462--475
[] $[]$ 
 []

File: figures/AppExtGraphics/PolarComplex-6.pdf Graphic file (type QTm)
<use  "figures/AppExtGraphics/PolarComplex-6.pdf" >
File: figures/AppExtGraphics/PolarComplex-7.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/PolarComplex-7.pdf" >
Overfull \hbox (2.99927pt too wide) in paragraph at lines 484--490
 [] 
 []

[474]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 502--503
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 502--503

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 521--522
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 521--522

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [475]
Overfull \hbox (1.21848pt too wide) in paragraph at lines 568--568
[] [] [] \OT1/cmr/m/n/10 = [] [] []$\EU1/Calibri(0)/m/n/10 . In rectangular for
m, the two square
 []

[476]
Overfull \hbox (15.86995pt too wide) in paragraph at lines 568--568
\EU1/Calibri(0)/m/n/10 and $[] \OT1/cmr/m/n/10 = []$\EU1/Calibri(0)/m/n/10 , we
 get the four fourth roots of $[]$ to be $[][] \OT1/cmr/m/n/10 = [] [] [] =
 []


Overfull \hbox (25.70126pt too wide) in paragraph at lines 568--568
[] [] []$\EU1/Calibri(0)/m/n/10 , $[][] \OT1/cmr/m/n/10 = [] [] [] = [] [] []$\
EU1/Calibri(0)/m/n/10 , $[][] \OT1/cmr/m/n/10 = [] [] [] =
 []

File: figures/AppExtGraphics/PolarComplex01.png Graphic file (type QTm)
<use  "figures/AppExtGraphics/PolarComplex01.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/AppExtGraphics/PolarComplex02.png Graphic file (type QTm)
<use  "figures/AppExtGraphics/PolarComplex02.png" >
Overfull \hbox (14.99959pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/AppExtGraphics/PolarComplex03.png Graphic file (type QTm)
<use  "figures/AppExtGraphics/PolarComplex03.png" >
Overfull \hbox (13.99959pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/AppExtGraphics/PolarComplex04.png Graphic file (type QTm)
<use  "figures/AppExtGraphics/PolarComplex04.png" >
Overfull \hbox (12.9996pt too wide) has occurred while \output is active
 [][][] 
 []

[477]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [478

] [479] [480])
Chapter 10.
(text/01_Limit_Introduction.tex
Underfull \hbox (badness 10000) in paragraph at lines 17--18

 []

File: figures/figZoomSinXOverX.pdf Graphic file (type QTm)
<use  "figures/figZoomSinXOverX.pdf" >
Overfull \hbox (7.9996pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/figSinXOverX.pdf Graphic file (type QTm)
<use  "figures/figSinXOverX.pdf" > [481




]
Underfull \hbox (badness 10000) in paragraph at lines 49--50

 []

(figures/sinx_over_x_table_1.tex) (figures/sinx_over_x_table_2.tex)
File: figures/figlimit1.pdf Graphic file (type QTm)

<use  "figures/figlimit1.pdf" >
Overfull \hbox (10.9996pt too wide) has occurred while \output is active
 [][][] 
 []

[482]
Underfull \hbox (badness 10000) in paragraph at lines 62--64

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--75

 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []


Underfull \hbox (badness 10000) in paragraph at lines 88--89

 []

(figures/table_limit1.tex)
File: figures/figlimit2.pdf Graphic file (type QTm)
 <use  "figures/figlimit2.pdf" >
(figures/table_limit2.tex) [483]
Underfull \hbox (badness 10000) in paragraph at lines 97--98

 []


Underfull \hbox (badness 10000) in paragraph at lines 110--111

 []


Underfull \hbox (badness 10000) in paragraph at lines 125--126

 []


Underfull \hbox (badness 10000) in paragraph at lines 138--139

 []

File: figures/figNoLimit3a.pdf Graphic file (type QTm)
<use  "figures/figNoLimit3a.pdf" >
File: figures/figNoLimit3b.pdf Graphic file (type QTm)
 <use  "figures/figNoLimit3b.pdf" >
Overfull \hbox (182.0pt too wide) in paragraph at lines 165--166
$[]$
 []


Underfull \hbox (badness 10000) in paragraph at lines 165--166

 []

File: figures/fignolimit1.pdf Graphic file (type QTm)
<use  "figures/fignolimit1.pdf" > (figures/table_nolimit1.tex)
File: figures/fignolimit2.pdf Graphic file (type QTm)

<use  "figures/fignolimit2.pdf" >
Overfull \hbox (2.99962pt too wide) has occurred while \output is active
 [][][] 
 []

(figures/table_nolimit2.tex) [484]
Underfull \hbox (badness 10000) in paragraph at lines 169--170

 []

File: figures/figDiffQuot1.pdf Graphic file (type QTm)
<use  "figures/figDiffQuot1.pdf" > [485]
Underfull \hbox (badness 10000) in paragraph at lines 212--213

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 232--233
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 232--233

 []

File: figures/figDiffQuotSmallha.pdf Graphic file (type QTm)
<use  "figures/figDiffQuotSmallha.pdf" >
File: figures/figDiffQuotSmallhb.pdf Graphic file (type QTm)

<use  "figures/figDiffQuotSmallhb.pdf" >
File: figures/figDiffQuotSmallhc.pdf Graphic file (type QTm)

<use  "figures/figDiffQuotSmallhc.pdf" >
Overfull \hbox (1.99965pt too wide) has occurred while \output is active
 [][][] 
 []


Underfull \hbox (badness 2005) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 10.16: |The difference quotient
 []

[486]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [487

]) (text/01_Analytic_Limits.tex
Overfull \hbox (1.35648pt too wide) in paragraph at lines 34--34
[]$[]$ [] 
 []


Overfull \hbox (16.35648pt too wide) in paragraph at lines 34--34
[]$[]$ [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 34--35
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 34--35

 []


Underfull \hbox (badness 10000) in paragraph at lines 38--39

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 66--66
[] [] 
 []

[488

]
Overfull \hbox (9.18732pt too wide) in paragraph at lines 66--66
[]\EU1/Calibri(0)/m/n/10 Using the Scalar Multiple and Sum/Difference rules, we
 find that $[] [][][]\OT1/cmr/m/n/10 ([]) +
 []


Underfull \hbox (badness 10000) in paragraph at lines 66--67

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 75--77
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []


Overfull \hbox (31.39998pt too wide) in paragraph at lines 120--121
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 120--121

 []

[489]
Overfull \hbox (1.50717pt too wide) in paragraph at lines 160--160
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 160--160

 []

[490]
Underfull \hbox (badness 10000) in paragraph at lines 160--161

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 168--169
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 168--169

 []


Overfull \hbox (9.55905pt too wide) in paragraph at lines 170--171
[]\EU1/Calibri(0)/m/n/10 It can take some work to figure out appropriate functi
ons by which to “squeeze”
 []


Underfull \hbox (badness 10000) in paragraph at lines 172--173

 []

File: figures/figSqueeze1.pdf Graphic file (type QTm)
<use  "figures/figSqueeze1.pdf" > [491]
File: figures/figSqueeze1a.pdf Graphic file (type QTm)
 <use  "figures/figSqueeze1a.pdf" >
File: figures/figSqueeze1b.pdf Graphic file (type QTm)

<use  "figures/figSqueeze1b.pdf" >
File: figures/figSqueeze1c.pdf Graphic file (type QTm)
 <use  "figures/figSqueeze1c.pdf" >
Overfull \hbox (1.555pt too wide) in paragraph at lines 202--202
 [] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 202--203

 []


Underfull \hbox (badness 10000) in paragraph at lines 206--207

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 223--223
[] [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 223--224
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 223--224

 []

[492]
Underfull \hbox (badness 10000) in paragraph at lines 229--230

 []


Underfull \hbox (badness 10000) in paragraph at lines 231--232

 []


Underfull \hbox (badness 10000) in paragraph at lines 245--246

 []

File: figures/fig_LimitXplus1.pdf Graphic file (type QTm)
<use  "figures/fig_LimitXplus1.pdf" > [493]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 249--250
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 249--250

 []


Underfull \hbox (badness 10000) in paragraph at lines 251--253

 []


Underfull \hbox (badness 10000) in paragraph at lines 264--265

 []


Underfull \hbox (badness 10000) in paragraph at lines 268--269

 []


Overfull \hbox (10.4779pt too wide) in paragraph at lines 284--284
[] 
 []

[494]
Underfull \hbox (badness 10000) in paragraph at lines 284--285

 []

[495]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [496

] [497]) (text/01_One_Sided_Limits.tex
Underfull \hbox (badness 10000) in paragraph at lines 50--50

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 50--54
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 50--54

 []


Underfull \hbox (badness 10000) in paragraph at lines 57--58

 []

[498

]
Overfull \hbox (1.50717pt too wide) in paragraph at lines 93--93
[] [] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 93--94

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 98--99
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 98--99

 []

File: figures/figOneSidedLimits1.pdf Graphic file (type QTm)
<use  "figures/figOneSidedLimits1.pdf" > [499]
Underfull \hbox (badness 10000) in paragraph at lines 102--103

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 138--138
[] [] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 138--139

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 159--159
[] [] 
 []

File: figures/figOneSidedLimits2.pdf Graphic file (type QTm)
<use  "figures/figOneSidedLimits2.pdf" >
File: figures/figOneSidedLimits3.pdf Graphic file (type QTm)

<use  "figures/figOneSidedLimits3.pdf" > [500]
Underfull \hbox (badness 10000) in paragraph at lines 159--160

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 183--183
[] [] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 183--184

 []

File: figures/figOneSidedLimits4.pdf Graphic file (type QTm)
<use  "figures/figOneSidedLimits4.pdf" > [501]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig01_04_ex_05.pdf Graphic file (type QTm)

<use  "figures/fig01_04_ex_05.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

File: figures/fig01_04_ex_06.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_06.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []

File: figures/fig01_04_ex_07.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_07.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

File: figures/fig01_04_ex_08.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_08.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

File: figures/fig01_04_ex_09.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_09.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

File: figures/fig01_04_ex_10.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_10.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

File: figures/fig01_04_ex_11.pdf Graphic file (type QTm)
<use  "figures/fig01_04_ex_11.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []

[502

]
File: figures/fig01_04_ex_12.pdf Graphic file (type QTm)
 <use  "figures/fig01_04_ex_12.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 197--197
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 197--197

 []


Overfull \vbox (8.69868pt too high) has occurred while \output is active []


[503]) (text/01_Continuity.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 10--11
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 10--11

 []


Underfull \hbox (badness 10000) in paragraph at lines 31--32

 []


Underfull \hbox (badness 10000) in paragraph at lines 48--48

 []

File: figures/figContinuous1.pdf Graphic file (type QTm)
<use  "figures/figContinuous1.pdf" >
File: figures/figContinuous2.pdf Graphic file (type QTm)
 <use  "figures/figContinuous2.pdf" >
[504

]
Underfull \hbox (badness 10000) in paragraph at lines 48--49

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 59--60
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 59--60

 []


Underfull \hbox (badness 10000) in paragraph at lines 61--66

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 93--93
[] [] 
 []

[505]
Underfull \hbox (badness 10000) in paragraph at lines 93--94

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 108--109
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 108--109

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 132--132
[] [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 132--133
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 132--133

 []


Underfull \hbox (badness 10000) in paragraph at lines 134--135

 []

[506]
Overfull \hbox (1.50717pt too wide) in paragraph at lines 162--162
[]$ $[]$
 []


Underfull \hbox (badness 10000) in paragraph at lines 162--162

 []


Overfull \hbox (3.39209pt too wide) in paragraph at lines 162--162
[]\EU1/Calibri(0)/m/n/10 The square–root terms are continuous on the intervals 
$\OT1/cmr/m/n/10 [[]\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 1\OT1/cmr/m/n/10 )$ \EU
1/Calibri(0)/m/n/10 and $\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@1\OML/cmm/m/it/10
 ; []\OT1/cmr/m/n/10 ]$\EU1/Calibri(0)/m/n/10 ,
 []


Underfull \hbox (badness 10000) in paragraph at lines 162--163

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 171--172
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 171--172

 []

File: figures/figContinuous3.pdf Graphic file (type QTm)
<use  "figures/figContinuous3.pdf" > [507

]
Underfull \hbox (badness 10000) in paragraph at lines 183--184

 []


Overfull \hbox (1.80075pt too wide) in paragraph at lines 218--218
[]$[]\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 
< []$\EU1/Calibri(0)/m/n/10 , $[]\OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 :[]\OT1/cm
r/m/n/10 ) \OML/cmm/m/it/10 > []$\EU1/Calibri(0)/m/n/10 , and at the midpoint, 
$[]\OML/cmm/m/it/10 :[][]$\EU1/Calibri(0)/m/n/10 , we have $[]\OT1/cmr/m/n/10 (
[]\OML/cmm/m/it/10 :[][]\OT1/cmr/m/n/10 ) \OML/cmm/m/it/10 >
 []


Underfull \hbox (badness 10000) in paragraph at lines 218--219

 []

File: figures/figXMinusCosX.pdf Graphic file (type QTm)
<use  "figures/figXMinusCosX.pdf" >
Overfull \hbox (7.9996pt too wide) has occurred while \output is active
 [][][] 
 []


Overfull \hbox (20.4892pt too wide) has occurred while \output is active
 [] 
 []

[508] [509]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig01_04_ex_05.pdf Graphic file (type QTm)
 <use  "figures/fig01_04_ex_05.pdf" >
File: figures/fig01_04_ex_06.pdf Graphic file (type QTm)

<use  "figures/fig01_04_ex_06.pdf" >
File: figures/fig01_04_ex_07.pdf Graphic file (type QTm)
 <use  "figures/fig01_04_ex_07.pdf" >
File: figures/fig01_04_ex_08.pdf Graphic file (type QTm)

<use  "figures/fig01_04_ex_08.pdf" >
File: figures/fig01_04_ex_09.pdf Graphic file (type QTm)
 <use  "figures/fig01_04_ex_09.pdf" >
File: figures/fig01_04_ex_10.pdf Graphic file (type QTm)

<use  "figures/fig01_04_ex_10.pdf" >
File: figures/fig01_04_ex_11.pdf Graphic file (type QTm)
 <use  "figures/fig01_04_ex_11.pdf" >
[510

]
Overfull \hbox (1.35645pt too wide) in paragraph at lines 233--233
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 233--233

 []

[511]) (text/01_Limits_Involving_Infinity.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 21--22
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 21--22

 []


Underfull \hbox (badness 10000) in paragraph at lines 25--26

 []


Underfull \hbox (badness 10000) in paragraph at lines 31--32

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/figoneoverxsquared.pdf Graphic file (type QTm)

<use  "figures/figoneoverxsquared.pdf" >
File: figures/fignolimit2.pdf Graphic file (type QTm)
 <use  "figures/fignolimit2.pdf" >
Overfull \hbox (2.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[512

]
Underfull \hbox (badness 10000) in paragraph at lines 44--45

 []


Underfull \hbox (badness 10000) in paragraph at lines 46--47

 []


Underfull \hbox (badness 10000) in paragraph at lines 53--54

 []


Underfull \hbox (badness 10000) in paragraph at lines 56--58

 []


Underfull \hbox (badness 10000) in paragraph at lines 61--62

 []

File: figures/figoneoverx.pdf Graphic file (type QTm)
<use  "figures/figoneoverx.pdf" >
File: figures/figmultipleasymptotes.pdf Graphic file (type QTm)
 <use  "figures/figmultipleasymptotes.pdf" >
File: figures/fignoasy.pdf Graphic file (type QTm)

<use  "figures/fignoasy.pdf" > [513]
Underfull \hbox (badness 10000) in paragraph at lines 66--67

 []


Underfull \hbox (badness 10000) in paragraph at lines 90--91

 []


Underfull \hbox (badness 10000) in paragraph at lines 107--107

 []


Underfull \hbox (badness 10000) in paragraph at lines 107--107

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 107--111
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 107--111

 []


Underfull \hbox (badness 10000) in paragraph at lines 113--114

 []

[514]
Underfull \hbox (badness 10000) in paragraph at lines 137--138

 []


Underfull \hbox (badness 10000) in paragraph at lines 147--148

 []

File: figures/fighzasy2.pdf Graphic file (type QTm)
<use  "figures/fighzasy2.pdf" >
File: figures/fighzasy3.pdf Graphic file (type QTm)
 <use  "figures/fighzasy3.pdf" >
File: figures/fighzasy4.pdf Graphic file (type QTm)

<use  "figures/fighzasy4.pdf" >
Overfull \hbox (53.9989pt too wide) in paragraph at lines 154--159
[][]
 []


Overfull \hbox (100.0pt too wide) in paragraph at lines 153--163
$[]$ 
 []


Underfull \hbox (badness 10000) in paragraph at lines 153--163

 []


Overfull \hbox (0.95432pt too wide) in paragraph at lines 167--168
\EU1/Calibri(0)/m/n/10 understand $[] []\OML/cmm/m/it/10 =[]$\EU1/Calibri(0)/m/
n/10 . As $[]$ gets larger and larger, the $[]\OML/cmm/m/it/10 =[]$ \EU1/Calibr
i(0)/m/n/10 gets smaller and smaller,
 []

File: figures/fighzasy1.pdf Graphic file (type QTm)
<use  "figures/fighzasy1.pdf" >
Overfull \hbox (7.99963pt too wide) has occurred while \output is active
 [][] 
 []

[515]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 199--200
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 199--200

 []

[516]
Underfull \hbox (badness 10000) in paragraph at lines 205--206

 []


Underfull \hbox (badness 10000) in paragraph at lines 218--219

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 262--262
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 262--262

 []


Underfull \hbox (badness 10000) in paragraph at lines 262--263

 []

File: figures/fighzasy5.pdf Graphic file (type QTm)
<use  "figures/fighzasy5.pdf" >
File: figures/fighzasy6.pdf Graphic file (type QTm)
 <use  "figures/fighzasy6.pdf" >
File: figures/fighzasy7.pdf Graphic file (type QTm)

<use  "figures/fighzasy7.pdf" >
Overfull \hbox (22.9996pt too wide) has occurred while \output is active
 [] 
 []

[517] [518

]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig01_06_ex_09.pdf Graphic file (type QTm)
 <use  "figures/fig01_06_ex_09.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 285--285
[][] [] 
 []

File: figures/fig01_06_ex_10.pdf Graphic file (type QTm)
<use  "figures/fig01_06_ex_10.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 285--285
[][] [] 
 []

File: figures/fig01_06_ex_11.pdf Graphic file (type QTm)
<use  "figures/fig01_06_ex_11.pdf" >
File: figures/fig01_06_ex_12.pdf Graphic file (type QTm)
 <use  "figures/fig01_06_ex_12.pdf" >
File: figures/fig01_06_ex_13.pdf Graphic file (type QTm)

<use  "figures/fig01_06_ex_13.pdf" >
File: figures/fig01_06_ex_40.pdf Graphic file (type QTm)
 <use  "figures/fig01_06_ex_40.pdf" >
[519

]
Overfull \hbox (1.35645pt too wide) in paragraph at lines 285--285
[][] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 285--285

 []

[520])
Chapter 11.
(text/02_Derivative.tex
Underfull \hbox (badness 10000) in paragraph at lines 7--8

 []

[521




]
Underfull \hbox (badness 10000) in paragraph at lines 52--53

 []

File: figures/figderivfalling.pdf Graphic file (type QTm)
<use  "figures/figderivfalling.pdf" >
File: figures/figderivfalling2.pdf Graphic file (type QTm)
 <use  "figures/figderivfalling2.pdf" >
File: figures/figderivfalling3.pdf Graphic file (type QTm)

<use  "figures/figderivfalling3.pdf" >
File: figures/figderivfalling4.pdf Graphic file (type QTm)
 <use  "figures/figderivfalling4.pdf" >
Overfull \hbox (21.9992pt too wide) in paragraph at lines 57--63
 [][] 
 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [522]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 70--71
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 70--71

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 72--73
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 72--73

 []


Underfull \hbox (badness 10000) in paragraph at lines 76--77

 []


Underfull \vbox (badness 1668) has occurred while \output is active []

 [523]
Overfull \hbox (1.50717pt too wide) in paragraph at lines 122--122
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 122--122

 []


Overfull \hbox (7.64705pt too wide) in paragraph at lines 122--122
[]\EU1/Calibri(0)/m/n/10 The tangent line at $[] \OT1/cmr/m/n/10 = []$ \EU1/Cal
ibri(0)/m/n/10 has slope $[][]$ and goes through the point $\OT1/cmr/m/n/10 ([]
\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ([])) =
 []


Underfull \hbox (badness 10000) in paragraph at lines 122--123

 []


Overfull \hbox (3.14627pt too wide) in paragraph at lines 124--125
[]\EU1/Calibri(0)/m/n/10 Another important line that can be created using infor
mation from the deriva-
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 129--130
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 129--130

 []


Underfull \vbox (badness 6141) has occurred while \output is active []

File: figures/figtangent1.pdf Graphic file (type QTm)

<use  "figures/figtangent1.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[524]
Underfull \hbox (badness 10000) in paragraph at lines 140--141

 []


Underfull \hbox (badness 10000) in paragraph at lines 144--145

 []


Underfull \vbox (badness 5939) has occurred while \output is active []

File: figures/fignormal1.pdf Graphic file (type QTm)

<use  "figures/fignormal1.pdf" > [525]
Underfull \hbox (badness 10000) in paragraph at lines 162--163

 []


Underfull \hbox (badness 10000) in paragraph at lines 165--168

 []


Underfull \hbox (badness 10000) in paragraph at lines 172--173

 []


Underfull \hbox (badness 10000) in paragraph at lines 174--175

 []

File: figures/figtangentsinx.pdf Graphic file (type QTm)
<use  "figures/figtangentsinx.pdf" > [526]
Underfull \hbox (badness 10000) in paragraph at lines 209--209

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 209--211
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 209--211

 []


Underfull \hbox (badness 10000) in paragraph at lines 212--213

 []


Underfull \hbox (badness 10000) in paragraph at lines 214--215

 []


Underfull \hbox (badness 10000) in paragraph at lines 227--228

 []

[527]
Underfull \hbox (badness 10000) in paragraph at lines 247--248

 []


Overfull \hbox (0.31468pt too wide) in paragraph at lines 265--265
[] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 265--266

 []

[528]
Underfull \hbox (badness 10000) in paragraph at lines 312--312

 []


Underfull \hbox (badness 10000) in paragraph at lines 312--312

 []


Overfull \hbox (2.00717pt too wide) in paragraph at lines 312--312
[][] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 312--313

 []


Underfull \hbox (badness 10000) in paragraph at lines 314--315

 []

File: figures/figabsolutevalue.pdf Graphic file (type QTm)
<use  "figures/figabsolutevalue.pdf" >
File: figures/figabsolutevalueprime.pdf Graphic file (type QTm)

<use  "figures/figabsolutevalueprime.pdf" > [529]
Underfull \hbox (badness 10000) in paragraph at lines 362--362

 []


Overfull \hbox (3.71289pt too wide) in paragraph at lines 362--362
$[]$ $[]$ $[]$ 
 []


Underfull \hbox (badness 10000) in paragraph at lines 362--363

 []

File: figures/figpiecewisesinx1.pdf Graphic file (type QTm)
<use  "figures/figpiecewisesinx1.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/figpiecewisecosx1.pdf Graphic file (type QTm)
<use  "figures/figpiecewisecosx1.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[530]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig02_01_ex_24.pdf Graphic file (type QTm)
 <use  "figures/fig02_01_ex_24.pdf" >
File: figures/fig02_01_ex_25.pdf Graphic file (type QTm)

<use  "figures/fig02_01_ex_25.pdf" >
File: figures/fig02_01_ex_26.pdf Graphic file (type QTm)
 <use  "figures/fig02_01_ex_26.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 369--369

 []

[531

]
File: figures/fig02_01_ex_27.pdf Graphic file (type QTm)
 <use  "figures/fig02_01_ex_27.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 369--369

 []

File: figures/fig02_01_ex_28.pdf Graphic file (type QTm)
<use  "figures/fig02_01_ex_28.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 369--369

 []

File: figures/fig02_01_ex_29.pdf Graphic file (type QTm)
<use  "figures/fig02_01_ex_29.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 369--369

 []

File: figures/fig02_01_ex_30.pdf Graphic file (type QTm)
<use  "figures/fig02_01_ex_30.pdf" >
Overfull \hbox (1.35645pt too wide) in paragraph at lines 369--369
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 369--369

 []


Underfull \hbox (badness 6316) in paragraph at lines 369--369
[]\EU1/Calibri(0)/m/n/9 Where is $[]$ continu-
 []


Overfull \hbox (1.35645pt too wide) in paragraph at lines 369--369
[] [] 
 []

File: figures/fig02_01_ex_34.pdf Graphic file (type QTm)
<use  "figures/fig02_01_ex_34.pdf" > [532]) (text/02_Derivative_Meaning.tex
Underfull \hbox (badness 10000) in paragraph at lines 8--9

 []


Underfull \hbox (badness 10000) in paragraph at lines 11--12

 []


Underfull \hbox (badness 10000) in paragraph at lines 17--18

 []


Underfull \hbox (badness 10000) in paragraph at lines 23--24

 []

[533

]
Underfull \hbox (badness 10000) in paragraph at lines 33--34

 []


Underfull \hbox (badness 10000) in paragraph at lines 45--45

 []


Overfull \hbox (0.2829pt too wide) in paragraph at lines 45--45
[]\EU1/Calibri(0)/m/n/10 What do $[]\OT1/cmr/m/n/10 ([][][][]) = [][][]$ \EU1/C
alibri(0)/m/n/10 and $[] []\OT1/cmr/m/n/10 ([][][][]) = []\OML/cmm/m/it/10 :[][
]$ \EU1/Calibri(0)/m/n/10 mean? Approximate $[]\OT1/cmr/m/n/10 ([][][][])$\EU1/
Calibri(0)/m/n/10 . 
 []


Underfull \hbox (badness 10000) in paragraph at lines 45--46

 []


Underfull \hbox (badness 10000) in paragraph at lines 48--49

 []


Underfull \hbox (badness 10000) in paragraph at lines 52--53

 []

[534]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 72--73
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 72--73

 []


Underfull \hbox (badness 10000) in paragraph at lines 77--78

 []


Underfull \hbox (badness 10000) in paragraph at lines 81--82

 []


Overfull \hbox (3.5102pt too wide) in paragraph at lines 92--92
[]$[]$\EU1/Calibri(0)/m/n/10 We can answer this directly after the following se
ction, where
 []


Underfull \vbox (badness 1436) has occurred while \output is active []

File: figures/figxsquared.pdf Graphic file (type QTm)

<use  "figures/figxsquared.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/figxsquaredwithgrid.pdf Graphic file (type QTm)
<use  "figures/figxsquaredwithgrid.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[535]
Underfull \hbox (badness 10000) in paragraph at lines 92--93

 []


Underfull \hbox (badness 10000) in paragraph at lines 119--120

 []


Underfull \hbox (badness 10000) in paragraph at lines 136--137

 []

File: figures/figfwithderiv.pdf Graphic file (type QTm)
<use  "figures/figfwithderiv.pdf" >
File: figures/figfwithderivdots.pdf Graphic file (type QTm)
 <use  "figures/figfwithderivdots.pdf" >
Overfull \hbox (16.99962pt too wide) has occurred while \output is active
 [][] 
 []

File: figures/figfwithderivzoom3.pdf Graphic file (type QTm)
<use  "figures/figfwithderivzoom3.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[536]
Underfull \hbox (badness 10000) in paragraph at lines 147--149

 []


Overfull \hbox (6.7248pt too wide) in paragraph at lines 153--154
[]\EU1/Calibri(0)/m/n/10 The importance of understanding the derivative cannot 
be understated. When
 []

[537]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig02_02_ex_15.pdf Graphic file (type QTm)
 <use  "figures/fig02_02_ex_15.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 155--155

 []

File: figures/fig02_02_ex_16.pdf Graphic file (type QTm)
<use  "figures/fig02_02_ex_16.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 155--155

 []

File: figures/fig02_02_ex_17.pdf Graphic file (type QTm)
<use  "figures/fig02_02_ex_17.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 155--155

 []

File: figures/fig02_02_ex_18.pdf Graphic file (type QTm)
<use  "figures/fig02_02_ex_18.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 155--155

 []

[538

]) (text/02_Derivative_Rules.tex
Underfull \hbox (badness 10000) in paragraph at lines 15--16

 []


Overfull \hbox (31.39998pt too wide) in paragraph at lines 41--42
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 41--42

 []


Overfull \hbox (80.0pt too wide) in paragraph at lines 20--44
$[]$ 
 []


Underfull \hbox (badness 10000) in paragraph at lines 47--48

 []

[539

]
Underfull \hbox (badness 10000) in paragraph at lines 50--51

 []


Underfull \hbox (badness 10000) in paragraph at lines 81--83

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 99--100
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 99--100

 []


Underfull \hbox (badness 10000) in paragraph at lines 108--109

 []

File: figures/figxcubedwithderiv.pdf Graphic file (type QTm)
<use  "figures/figxcubedwithderiv.pdf" > [540]
Underfull \hbox (badness 10000) in paragraph at lines 123--124

 []


Underfull \hbox (badness 10000) in paragraph at lines 127--128

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 144--146
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 144--146

 []


Underfull \hbox (badness 10000) in paragraph at lines 147--148

 []


Underfull \hbox (badness 4132) has occurred while \output is active
[]\EU1/Calibri(0)/bx/n/9 Note: \EU1/Calibri(0)/m/n/9 Definition []69[] comes wi
th the
 []

[541]
Underfull \hbox (badness 10000) in paragraph at lines 149--150

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 175--175
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 175--175

 []


Overfull \hbox (20.0098pt too wide) detected at line 175
[] []\OT1/cmr/m/n/10 ([]) = [] [];  [] []([]) = \OMS/cmsy/m/n/10 ^^@ [] []\OT1/
cmr/m/n/10 ;  [] []([]) = \OMS/cmsy/m/n/10 ^^@ [] []\OT1/cmr/m/n/10 ;  [] []([]
) = [] []\OML/cmm/m/it/10 :
 []


Underfull \hbox (badness 10000) in paragraph at lines 177--178

 []

[542] [543]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


Overfull \hbox (1.35645pt too wide) in paragraph at lines 194--194
[] []
 []


Underfull \hbox (badness 10000) in paragraph at lines 194--194

 []


Overfull \vbox (4.9724pt too high) has occurred while \output is active []


[544

]) (text/02_Product_Quotient_Rules.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 8--9
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 8--9

 []


Underfull \hbox (badness 10000) in paragraph at lines 12--13

 []


Underfull \hbox (badness 10000) in paragraph at lines 20--21

 []


Underfull \hbox (badness 10000) in paragraph at lines 22--23

 []


Overfull \hbox (3.55066pt too wide) in paragraph at lines 39--39
[] 
 []

File: figures/fig5xsquaredsinx.pdf Graphic file (type QTm)
<use  "figures/fig5xsquaredsinx.pdf" >
Overfull \hbox (1.99962pt too wide) has occurred while \output is active
 [][][] 
 []

[545

]
Underfull \hbox (badness 10000) in paragraph at lines 39--40

 []


Underfull \hbox (badness 10000) in paragraph at lines 41--42

 []


Underfull \hbox (badness 10000) in paragraph at lines 54--55

 []

[546]
Underfull \hbox (badness 10000) in paragraph at lines 67--68

 []


Underfull \hbox (badness 10000) in paragraph at lines 69--70

 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []


Underfull \hbox (badness 10000) in paragraph at lines 87--88

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 91--92
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 91--92

 []


Underfull \hbox (badness 10000) in paragraph at lines 93--94

 []

[547]
Underfull \hbox (badness 10000) in paragraph at lines 95--96

 []


Underfull \hbox (badness 10000) in paragraph at lines 105--106

 []


Underfull \hbox (badness 10000) in paragraph at lines 107--108

 []


Underfull \hbox (badness 10000) in paragraph at lines 121--122

 []


Overfull \hbox (1.50717pt too wide) in paragraph at lines 140--140
[] [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 140--141
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 140--141

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/figtanx.pdf Graphic file (type QTm)

<use  "figures/figtanx.pdf" > [548]
Underfull \hbox (badness 10000) in paragraph at lines 142--143

 []


Overfull \hbox (13.48161pt too wide) in paragraph at lines 155--155
[]$[]$\EU1/Calibri(0)/m/n/10 We found in Example []241[] that the $[] []\OT1/cm
r/m/n/10 ([]) = []$\EU1/Calibri(0)/m/n/10 .
 []


Underfull \hbox (badness 10000) in paragraph at lines 155--156

 []


Underfull \hbox (badness 10000) in paragraph at lines 157--158

 []

[549]
Underfull \hbox (badness 10000) in paragraph at lines 172--173

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 184--185
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 184--185

 []


Underfull \hbox (badness 10000) in paragraph at lines 186--187

 []


Underfull \vbox (badness 1406) has occurred while \output is active []

 [550]
Underfull \hbox (badness 10000) in paragraph at lines 210--211

 []

[551]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [552

]
File: figures/fig02_04_ex_42.pdf Graphic file (type QTm)
 <use  "figures/fig02_04_ex_42.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 217--217

 []

File: figures/fig02_04_ex_43.pdf Graphic file (type QTm)
<use  "figures/fig02_04_ex_43.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 217--217

 []

File: figures/fig02_04_ex_44.pdf Graphic file (type QTm)
<use  "figures/fig02_04_ex_44.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 217--217

 []

File: figures/fig02_04_ex_45.pdf Graphic file (type QTm)
<use  "figures/fig02_04_ex_45.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 217--217

 []

[553]) (text/02_Chain_Rule.tex
Underfull \hbox (badness 10000) in paragraph at lines 12--13

 []


Underfull \hbox (badness 10000) in paragraph at lines 40--40

 []


Underfull \hbox (badness 10000) in paragraph at lines 40--40

 []


Underfull \hbox (badness 10000) in paragraph at lines 40--41

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 45--46
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 45--46

 []


Underfull \vbox (badness 1342) has occurred while \output is active []

 [554

]
Underfull \hbox (badness 10000) in paragraph at lines 51--52

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--74

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--74

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--74

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--74

 []


Underfull \hbox (badness 10000) in paragraph at lines 74--75

 []


Underfull \hbox (badness 10000) in paragraph at lines 76--77

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 80--81
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 80--81

 []

[555]
Underfull \hbox (badness 10000) in paragraph at lines 88--89

 []


Underfull \hbox (badness 10000) in paragraph at lines 120--121

 []


Underfull \hbox (badness 10000) in paragraph at lines 130--131

 []

File: figures/figchain7.pdf Graphic file (type QTm)
<use  "figures/figchain7.pdf" > [556]
Overfull \hbox (1.50717pt too wide) in paragraph at lines 138--151
[] [] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 138--151

 []


Underfull \hbox (badness 10000) in paragraph at lines 152--153

 []


Underfull \hbox (badness 10000) in paragraph at lines 169--169

 []


Underfull \hbox (badness 10000) in paragraph at lines 169--170

 []


Underfull \hbox (badness 10000) in paragraph at lines 175--176

 []

[557]
Underfull \hbox (badness 10000) in paragraph at lines 189--191

 []


Underfull \hbox (badness 10000) in paragraph at lines 192--193

 []


Underfull \hbox (badness 10000) in paragraph at lines 211--211

 []


Underfull \hbox (badness 10000) in paragraph at lines 211--212

 []


Underfull \hbox (badness 10000) in paragraph at lines 243--244

 []

[558]
Underfull \hbox (badness 10000) in paragraph at lines 270--271

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 276--277
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 276--277

 []


Underfull \hbox (badness 10000) in paragraph at lines 344--345

 []

[559]
Underfull \hbox (badness 10000) in paragraph at lines 375--377

 []

File: figures/figchainrulegears.pdf Graphic file (type QTm)
<use  "figures/figchainrulegears.pdf" > [560]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [561

]) [562



]
Chapter 12.
(text/03_Extreme_Values.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 17--18
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 17--18

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 54--55
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 54--55

 []


Underfull \hbox (badness 10000) in paragraph at lines 56--57

 []

File: figures/figextreme1.pdf Graphic file (type QTm)
<use  "figures/figextreme1.pdf" >
File: figures/figextreme2.pdf Graphic file (type QTm)
 <use  "figures/figextreme2.pdf" >
File: figures/figextreme3.pdf Graphic file (type QTm)

<use  "figures/figextreme3.pdf" >
Overfull \hbox (3.99965pt too wide) has occurred while \output is active
 [][][] 
 []

[563

]
Underfull \hbox (badness 10000) in paragraph at lines 63--64

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 82--84
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 82--84

 []


Underfull \hbox (badness 10000) in paragraph at lines 87--88

 []


Underfull \hbox (badness 10000) in paragraph at lines 100--101

 []


Underfull \hbox (badness 10000) in paragraph at lines 109--110

 []

File: figures/figextval1.pdf Graphic file (type QTm)
<use  "figures/figextval1.pdf" >
File: figures/figextval2.pdf Graphic file (type QTm)
 <use  "figures/figextval2.pdf" >
File: figures/figextval3.pdf Graphic file (type QTm)

<use  "figures/figextval3.pdf" > [564]
Underfull \hbox (badness 10000) in paragraph at lines 117--117

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 117--118
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 117--118

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 121--122
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 121--122

 []


Underfull \hbox (badness 10000) in paragraph at lines 123--124

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 137--140
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 137--140

 []

File: figures/figextreme4.pdf Graphic file (type QTm)
<use  "figures/figextreme4.pdf" >
File: figures/figextval4.pdf Graphic file (type QTm)
 <use  "figures/figextval4.pdf" > [565]
Underfull \hbox (badness 10000) in paragraph at lines 151--152

 []


Underfull \hbox (badness 10000) in paragraph at lines 157--158

 []


Underfull \vbox (badness 4752) has occurred while \output is active []

File: figures/figextval5.pdf Graphic file (type QTm)

<use  "figures/figextval5.pdf" > [566]
Overfull \hbox (14.92125pt too wide) in paragraph at lines 189--189
\EU1/Calibri(0)/m/n/10 always positive so we ignore $\OMS/cmsy/m/n/10 ^^@[]$\EU
1/Calibri(0)/m/n/10 , etc.) So $[]\OT1/cmr/m/n/10 ([][]) = []$ \EU1/Calibri(0)/
m/n/10 when $[] \OT1/cmr/m/n/10 = []\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 ^^F[]\O
ML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 ^^F[]\OML/cmm/m/it/10 ; []$\EU1/Calibri(0)/m/
n/10 .
 []


Underfull \hbox (badness 10000) in paragraph at lines 189--190

 []


Underfull \hbox (badness 10000) in paragraph at lines 191--192

 []


Underfull \hbox (badness 10000) in paragraph at lines 202--203

 []


Underfull \hbox (badness 2111) has occurred while \output is active
[]\EU1/Calibri(0)/m/n/9 Figure 12.10: |Finding the extrema of
 []

File: figures/figextval6.pdf Graphic file (type QTm)
<use  "figures/figextval6.pdf" >
File: figures/figextval7.pdf Graphic file (type QTm)
 <use  "figures/figextval7.pdf" > [567]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

File: figures/fig03_01_ex_06.pdf Graphic file (type QTm)

<use  "figures/fig03_01_ex_06.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 211--211

 []

File: figures/fig03_01_ex_07.pdf Graphic file (type QTm)
<use  "figures/fig03_01_ex_07.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 211--211

 []

File: figures/fig03_01_ex_08.pdf Graphic file (type QTm)
<use  "figures/fig03_01_ex_08.pdf" >
File: figures/fig03_01_ex_09.pdf Graphic file (type QTm)
 <use  "figures/fig03_01_ex_09.pdf" >
File: figures/fig03_01_ex_10.pdf Graphic file (type QTm)

<use  "figures/fig03_01_ex_10.pdf" >
File: figures/fig03_01_ex_11.pdf Graphic file (type QTm)
 <use  "figures/fig03_01_ex_11.pdf" >
File: figures/fig03_01_ex_12.pdf Graphic file (type QTm)

<use  "figures/fig03_01_ex_12.pdf" >
File: figures/fig03_01_ex_13.pdf Graphic file (type QTm)
 <use  "figures/fig03_01_ex_13.pdf" >
File: figures/fig03_01_ex_14.pdf Graphic file (type QTm)

<use  "figures/fig03_01_ex_14.pdf" > [568

] [569])
(text/03_Increasing_Decreasing.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 19--20
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 19--20

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 43--44
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 43--44

 []

File: figures/figincr0.pdf Graphic file (type QTm)
<use  "figures/figincr0.pdf" >
File: figures/figincr00.pdf Graphic file (type QTm)
 <use  "figures/figincr00.pdf" > [570

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 60--61
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 60--61

 []


Underfull \hbox (badness 10000) in paragraph at lines 62--63

 []


Underfull \hbox (badness 10000) in paragraph at lines 88--88

 []

File: figures/figincrline1.pdf Graphic file (type QTm)
<use  "figures/figincrline1.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 88--88

 []

[571]
Underfull \hbox (badness 10000) in paragraph at lines 88--88

 []


Underfull \hbox (badness 10000) in paragraph at lines 88--88

 []


Overfull \hbox (3.52487pt too wide) in paragraph at lines 88--89
[]\EU1/Calibri(0)/m/n/10 We can verify our calculations by considering Figure [
]12.17[], where $[]$ is graphed.
 []


Underfull \hbox (badness 10000) in paragraph at lines 88--89

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

File: figures/figincr1.pdf Graphic file (type QTm)

<use  "figures/figincr1.pdf" > [572]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 113--116
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 113--116

 []

[573]
File: figures/figincrline2.pdf Graphic file (type QTm)
 <use  "figures/figincrline2.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 151--152

 []


Underfull \hbox (badness 10000) in paragraph at lines 155--156

 []


Underfull \hbox (badness 10000) in paragraph at lines 194--194

 []

File: figures/figincr2.pdf Graphic file (type QTm)
<use  "figures/figincr2.pdf" > [574]
Underfull \hbox (badness 10000) in paragraph at lines 194--194

 []

File: figures/figincrline3.pdf Graphic file (type QTm)
<use  "figures/figincrline3.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 194--194

 []


Underfull \hbox (badness 10000) in paragraph at lines 194--195

 []

File: figures/figincr3.pdf Graphic file (type QTm)
<use  "figures/figincr3.pdf" > [575]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [576

]) (text/03_Concavity.tex
Underfull \hbox (badness 10000) in paragraph at lines 7--8

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 17--18
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 17--18

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 50--51
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 50--51

 []

File: figures/figconcavity1.pdf Graphic file (type QTm)
<use  "figures/figconcavity1.pdf" >
File: figures/figconcavity2.pdf Graphic file (type QTm)
 <use  "figures/figconcavity2.pdf" >
Underfull \hbox (badness 3158) has occurred while \output is active
[]\EU1/Calibri(0)/bx/n/9 Note: \EU1/Calibri(0)/m/n/9 A mnemonic for remembering

 []

[577

]
Overfull \hbox (1.39998pt too wide) in paragraph at lines 72--73
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 72--73

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 81--82
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 81--82

 []


Underfull \hbox (badness 10000) in paragraph at lines 83--84

 []


Underfull \hbox (badness 10000) in paragraph at lines 97--99

 []

File: figures/figconcavity3.pdf Graphic file (type QTm)
<use  "figures/figconcavity3.pdf" >
Underfull \hbox (badness 5985) has occurred while \output is active
\EU1/Calibri(0)/m/n/9 that concavity interacts with increas-
 []

File: figures/figconcavity4.pdf Graphic file (type QTm)
<use  "figures/figconcavity4.pdf" >
File: figures/figconcline1.pdf Graphic file (type QTm)
 <use  "figures/figconcline1.pdf" >
File: figures/figconc1.pdf Graphic file (type QTm)

<use  "figures/figconc1.pdf" > [578]
Underfull \hbox (badness 10000) in paragraph at lines 128--128

 []

File: figures/figconcline2.pdf Graphic file (type QTm)
<use  "figures/figconcline2.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 128--128

 []


Underfull \hbox (badness 10000) in paragraph at lines 128--130

 []


Underfull \hbox (badness 10000) in paragraph at lines 135--136

 []

File: figures/figconc2.pdf Graphic file (type QTm)
<use  "figures/figconc2.pdf" >
File: figures/figconc3.pdf Graphic file (type QTm)
 <use  "figures/figconc3.pdf" > [579]
Underfull \hbox (badness 10000) in paragraph at lines 149--150

 []


Underfull \hbox (badness 10000) in paragraph at lines 154--155

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 180--181
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 180--181

 []


Underfull \hbox (badness 10000) in paragraph at lines 186--187

 []

File: figures/figconc3b.pdf Graphic file (type QTm)
<use  "figures/figconc3b.pdf" >
Overfull \hbox (2.99962pt too wide) has occurred while \output is active
 [][][] 
 []

File: figures/figconcavity5.pdf Graphic file (type QTm)
<use  "figures/figconcavity5.pdf" >
File: figures/figconcavity6.pdf Graphic file (type QTm)
 <use  "figures/figconcavity6.pdf" >
[580]
Underfull \hbox (badness 10000) in paragraph at lines 191--192

 []

File: figures/figconc4.pdf Graphic file (type QTm)
<use  "figures/figconc4.pdf" > [581

]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [582

] [583]) (text/03_Curve_Sketching.tex
Overfull \hbox (1.39998pt too wide) in paragraph at lines 29--42
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 29--42

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 42--45
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 42--45

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [584

]
File: figures/figsketchline1.pdf Graphic file (type QTm)

<use  "figures/figsketchline1.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 94--94
$[]$ 
 []

File: figures/figsketch1a.pdf Graphic file (type QTm)
<use  "figures/figsketch1a.pdf" >
File: figures/figsketch1b.pdf Graphic file (type QTm)
 <use  "figures/figsketch1b.pdf" >
File: figures/figsketch1.pdf Graphic file (type QTm)

<use  "figures/figsketch1.pdf" >
Overfull \hbox (3.99965pt too wide) has occurred while \output is active
 [][] 
 []

[585]
Overfull \hbox (2.93321pt too wide) in paragraph at lines 154--154
[]\EU1/Calibri(0)/m/n/10 There is a horizontal asymptote of $[] \OT1/cmr/m/n/10
 = []$\EU1/Calibri(0)/m/n/10 , as $[] []\OT1/cmr/m/n/10 ([]) = []$ \EU1/Calibri
(0)/m/n/10 and $[] []\OT1/cmr/m/n/10 ([]) =
 []

File: figures/figsketchline2.pdf Graphic file (type QTm)
<use  "figures/figsketchline2.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 154--154
$[]$ 
 []

File: figures/figsketch2a.pdf Graphic file (type QTm)
<use  "figures/figsketch2a.pdf" >
File: figures/figsketch2b.pdf Graphic file (type QTm)
 <use  "figures/figsketch2b.pdf" >
File: figures/figsketch2.pdf Graphic file (type QTm)

<use  "figures/figsketch2.pdf" >
Overfull \hbox (1.99965pt too wide) has occurred while \output is active
 [][] 
 []

[586]
File: figures/figsketchline3.pdf Graphic file (type QTm)
 <use  "figures/figsketchline3.pdf" >
Overfull \hbox (25.00003pt too wide) in paragraph at lines 204--204
$[]$ 
 []


Underfull \hbox (badness 10000) in paragraph at lines 204--205

 []

File: figures/figsketch3a.pdf Graphic file (type QTm)
<use  "figures/figsketch3a.pdf" >
File: figures/figsketch3b.pdf Graphic file (type QTm)
 <use  "figures/figsketch3b.pdf" >
File: figures/figsketch3.pdf Graphic file (type QTm)

<use  "figures/figsketch3.pdf" >
Overfull \hbox (1.99965pt too wide) has occurred while \output is active
 [][] 
 []

[587]
File: figures/figmathematica_sinx.pdf Graphic file (type QTm)
 <use  "figures/figmathematica_sinx.pdf" >
Overfull \hbox (3.80219pt too wide) in paragraph at lines 227--228
[]\EU1/Calibri(0)/m/n/10 There are many applications of our understanding of de
rivatives beyond curve
 []

[588]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [589

]) (text/05_Antiderivatives.tex
Underfull \hbox (badness 10000) in paragraph at lines 22--22

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 22--23
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 22--23

 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 30--31
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 30--31

 []

[590

]
File: figures/figanti1.pdf Graphic file (type QTm)
 <use  "figures/figanti1.pdf" >
Underfull \hbox (badness 10000) in paragraph at lines 46--47

 []


Overfull \hbox (25.23961pt too wide) in paragraph at lines 55--55
[] []$\EU1/Calibri(0)/m/n/10 . Some thought will lead us to one solution: $[]\O
T1/cmr/m/n/10 ([]) = \OMS/cmsy/m/n/10 ^^@ [] []$\EU1/Calibri(0)/m/n/10 , becaus
e $[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 ^^@ [] []\OT1/cmr/m/n/10 ) =
 []


Underfull \hbox (badness 10000) in paragraph at lines 55--56

 []

[591]
Underfull \hbox (badness 10000) in paragraph at lines 68--69

 []


Underfull \hbox (badness 10000) in paragraph at lines 85--86

 []

\bh=\skip95
\bd=\skip96

Overfull \hbox (1.50717pt too wide) in paragraph at lines 149--149
[][] [] 
 []


Overfull \hbox (1.39998pt too wide) in paragraph at lines 149--196
[][][]
 []


Underfull \hbox (badness 10000) in paragraph at lines 149--196

 []


Underfull \vbox (badness 10000) has occurred while \output is active []

 [592]
[593]
Underfull \hbox (badness 10000) in paragraph at lines 229--230

 []

[594]
Underfull \hbox (badness 10000) in paragraph at lines 253--254

 []


Underfull \hbox (badness 10000) in paragraph at lines 275--276

 []

[595]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 [596

] [597]) [598



]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 470.295pt, 72.0pt)
* v-part:(T,H,B)=(54.2025pt, 668.4975pt, 72.26999pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=470.295pt
* \textheight=668.4975pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-0.26999pt
* \topmargin=-48.13498pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)


Appendix A.
(Math1010text.answers
File: figures/RelationsandFunctionsGraphics/CartesianPlane-36.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-36.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-37.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-37.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-38.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-38.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-39.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-39.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-40.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-40.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-41.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-41.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-42.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-42.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-43.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-43.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-44.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-44.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-45.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-45.pdf" >
File: figures/RelationsandFunctionsGraphics/CartesianPlane-46.pdf Graphic file 
(type QTm)

<use  "figures/RelationsandFunctionsGraphics/CartesianPlane-46.pdf" > [1




]
File: figures/RelationsandFunctionsGraphics/Relations-23.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-23.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-25.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-25.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-27.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-27.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-29.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-29.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-31.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-31.pdf" > [2]
File: figures/RelationsandFunctionsGraphics/Relations-33.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-33.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-35.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-35.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-37.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-37.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-39.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-39.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-41.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-41.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-43.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-43.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-45.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-45.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-47.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-47.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-49.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-49.pdf" > [3]
File: figures/RelationsandFunctionsGraphics/Relations-51.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-51.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-53.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-53.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-55.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-55.pdf" >
File: figures/RelationsandFunctionsGraphics/Relations-57.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-57.pdf" > [4]
File: figures/RelationsandFunctionsGraphics/Relations-59.pdf Graphic file (type
 QTm)

<use  "figures/RelationsandFunctionsGraphics/Relations-59.pdf" > [5] [6]
[7]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-17.pdf Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-17.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-19.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-19.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-21.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-21.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-23.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-23.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-25.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-25.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-27.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-27.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-29.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-29.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-31.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-31.pdf" >
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-33.pdf Graphic fi
le (type QTm)

<use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-33.pdf" >
[8]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-35.pdf Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-35.pdf" >
[9]
File: figures/RelationsandFunctionsGraphics/GraphsofFunctions-37.pdf Graphic fi
le (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/GraphsofFunctions-37.pdf" >
[10]
File: figures/RelationsandFunctionsGraphics/Transformations-59.pdf Graphic file
 (type QTm)
 <use  "figures/RelationsandFunctionsGraphics/Transformations-59.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-61.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-61.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-63.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-63.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-65.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-65.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-67.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-67.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-69.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-69.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-71.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-71.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-73.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-73.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-75.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-75.pdf" > [11]
File: figures/RelationsandFunctionsGraphics/Transformations-77.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-77.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-79.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-79.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-81.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-81.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-83.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-83.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-85.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-85.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-87.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-87.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-89.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-89.pdf" >
File: figures/RelationsandFunctionsGraphics/Transformations-91.pdf Graphic file
 (type QTm)

<use  "figures/RelationsandFunctionsGraphics/Transformations-91.pdf" > [12]
File: figures/LinearQuadraticGraphics/LinearFunctions-17.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-17.pdf" >
File: figures/LinearQuadraticGraphics/LinearFunctions-19.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-19.pdf" >
File: figures/LinearQuadraticGraphics/LinearFunctions-21.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-21.pdf" >

LaTeX Warning: Command \nobreakspace invalid in math mode on input line 30.

File: figures/LinearQuadraticGraphics/LinearFunctions-23.pdf Graphic file (type
 QTm)
<use  "figures/LinearQuadraticGraphics/LinearFunctions-23.pdf" >
File: figures/LinearQuadraticGraphics/LinearFunctions-24.pdf Graphic file (type
 QTm)

<use  "figures/LinearQuadraticGraphics/LinearFunctions-24.pdf" > [13]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-19.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-19.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-21.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-21.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-23.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-23.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-25.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-25.pdf" >
[14]
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-27.pdf Graphic fil
e (type QTm)
 <use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-27.pdf" >
File: figures/LinearQuadraticGraphics/AbsoluteValueFunctions-29.pdf Graphic fil
e (type QTm)

<use  "figures/LinearQuadraticGraphics/AbsoluteValueFunctions-29.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-14.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-14.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-16.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-16.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-18.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-18.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-20.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-20.pdf" > [15]
File: figures/LinearQuadraticGraphics/QuadraticFunctions-22.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-22.pdf" >
File: figures/LinearQuadraticGraphics/QuadraticFunctions-23.pdf Graphic file (t
ype QTm)

<use  "figures/LinearQuadraticGraphics/QuadraticFunctions-23.pdf" > [16]
File: figures/LinearQuadraticGraphics/Inequalities-27.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-27.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-29.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-29.pdf" >
File: figures/LinearQuadraticGraphics/Inequalities-31.pdf Graphic file (type QT
m)

<use  "figures/LinearQuadraticGraphics/Inequalities-31.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-21.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-21.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-23.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-23.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-25.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-25.pdf" > [17]
File: figures/PolynomialsGraphics/GraphsofPolynomials-27.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-27.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-29.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-29.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-31.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-31.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-33.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-33.pdf" >
File: figures/PolynomialsGraphics/GraphsofPolynomials-35.pdf Graphic file (type
 QTm)

<use  "figures/PolynomialsGraphics/GraphsofPolynomials-35.pdf" > [18] [19]
[20]
File: figures/RationalsGraphics/RationalGraphs-17.pdf Graphic file (type QTm)
 <use  "figures/RationalsGraphics/RationalGraphs-17.pdf" >
File: figures/RationalsGraphics/RationalGraphs-19.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-19.pdf" >
File: figures/RationalsGraphics/RationalGraphs-21.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-21.pdf" >
File: figures/RationalsGraphics/RationalGraphs-23.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-23.pdf" > [21]
File: figures/RationalsGraphics/RationalGraphs-25.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-25.pdf" >
File: figures/RationalsGraphics/RationalGraphs-27.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-27.pdf" >
File: figures/RationalsGraphics/RationalGraphs-29.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-29.pdf" >
File: figures/RationalsGraphics/RationalGraphs-31.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-31.pdf" >
File: figures/RationalsGraphics/RationalGraphs-33.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-33.pdf" > [22]
File: figures/RationalsGraphics/RationalGraphs-35.pdf Graphic file (type QTm)

<use  "figures/RationalsGraphics/RationalGraphs-35.pdf" > [23]
File: figures/FurtherGraphics/AlgebraicFunctions-16.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-16.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-17.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-17.pdf" > [24]
File: figures/FurtherGraphics/AlgebraicFunctions-20.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-20.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-21.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-21.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-24.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-24.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-25.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-25.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-28.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-28.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-29.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-29.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-32.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-32.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-33.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-33.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-36.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-36.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-38.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-38.pdf" >
File: figures/FurtherGraphics/AlgebraicFunctions-40.pdf Graphic file (type QTm)


<use  "figures/FurtherGraphics/AlgebraicFunctions-40.pdf" > [25]
File: figures/FurtherGraphics/WINDCHILL.jpg Graphic file (type QTm)

<use  "figures/FurtherGraphics/WINDCHILL.jpg" >
File: figures/ExpLogsGraphics/IntroExpLogs-21.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-21.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-23.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-23.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-25.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-25.pdf" > [26]
File: figures/ExpLogsGraphics/IntroExpLogs-27.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-27.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-29.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-29.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-31.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-31.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-32.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-32.pdf" >
File: figures/ExpLogsGraphics/IntroExpLogs-34.pdf Graphic file (type QTm)

<use  "figures/ExpLogsGraphics/IntroExpLogs-34.pdf" > [27] [28]
File: figures/IntroTrigGraphics/Angles-41.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-41.pdf" >
File: figures/IntroTrigGraphics/Angles-43.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-43.pdf" >
File: figures/IntroTrigGraphics/Angles-45.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-45.pdf" >
File: figures/IntroTrigGraphics/Angles-47.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-47.pdf" >
File: figures/IntroTrigGraphics/Angles-49.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-49.pdf" >
File: figures/IntroTrigGraphics/Angles-51.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-51.pdf" > [29]
File: figures/IntroTrigGraphics/Angles-53.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-53.pdf" >
File: figures/IntroTrigGraphics/Angles-55.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-55.pdf" >
File: figures/IntroTrigGraphics/Angles-57.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-57.pdf" >
File: figures/IntroTrigGraphics/Angles-59.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-59.pdf" >
File: figures/IntroTrigGraphics/Angles-61.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-61.pdf" >
File: figures/IntroTrigGraphics/Angles-63.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-63.pdf" >
File: figures/IntroTrigGraphics/Angles-65.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/Angles-65.pdf" > [30] [31] [32] [33] [34]
[35]
File: figures/IntroTrigGraphics/TrigGraphs-22.pdf Graphic file (type QTm)
 <use  "figures/IntroTrigGraphics/TrigGraphs-22.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-24.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-24.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-26.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-26.pdf" > [36]
File: figures/IntroTrigGraphics/TrigGraphs-28.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-28.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-30.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-30.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-32.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-32.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-34.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-34.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-36.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-36.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-38.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-38.pdf" > [37]
File: figures/IntroTrigGraphics/TrigGraphs-40.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-40.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-42.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-42.pdf" >
File: figures/IntroTrigGraphics/TrigGraphs-44.pdf Graphic file (type QTm)

<use  "figures/IntroTrigGraphics/TrigGraphs-44.pdf" > [38] [39] [40]
Overfull \hbox (4.10933pt too wide) in paragraph at lines 92--92
[] []$  
 []

[41] [42]
File: figures/AppExtGraphics/IntroPolar-41.pdf Graphic file (type QTm)
 <use  "figures/AppExtGraphics/IntroPolar-41.pdf" >
File: figures/AppExtGraphics/IntroPolar-43.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-43.pdf" >
File: figures/AppExtGraphics/IntroPolar-45.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-45.pdf" >
File: figures/AppExtGraphics/IntroPolar-47.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-47.pdf" >
File: figures/AppExtGraphics/IntroPolar-49.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-49.pdf" >
File: figures/AppExtGraphics/IntroPolar-51.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-51.pdf" > [43]
File: figures/AppExtGraphics/IntroPolar-53.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-53.pdf" >
File: figures/AppExtGraphics/IntroPolar-55.pdf Graphic file (type QTm)

<use  "figures/AppExtGraphics/IntroPolar-55.pdf" > [44] [45] [46]
File: figures/fig02_01_ex_27ans.pdf Graphic file (type QTm)

<use  "figures/fig02_01_ex_27ans.pdf" >
File: figures/fig02_01_ex_29ans.pdf Graphic file (type QTm)

<use  "figures/fig02_01_ex_29ans.pdf" > [47]
File: figures/fig02_04_ex_43a.pdf Graphic file (type QTm)

<use  "figures/fig02_04_ex_43a.pdf" >
File: figures/fig02_04_ex_45a.pdf Graphic file (type QTm)
 <use  "figures/fig02_04_ex_45a.pdf" >
[48] [49]) [50]
*geometry* verbose mode - [ newgeometry ] result:
* driver: pdftex
* paper: custom
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: twoside 
* h-part:(L,W,R)=(72.0pt, 506.295pt, 36.0pt)
* v-part:(T,H,B)=(28.90799pt, 722.7pt, 43.362pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=506.295pt
* \textheight=722.7pt
* \oddsidemargin=-0.26999pt
* \evensidemargin=-36.26999pt
* \topmargin=-73.42949pt
* \headheight=12.0pt
* \headsep=18.06749pt
* \topskip=10.0pt
* \footskip=29.0pt
* \marginparwidth=150.0pt
* \marginparsep=32.0pt
* \columnsep=20.0pt
* \skip\footins=9.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidetrue
* \@mparswitchtrue
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

 (Math1010text.ind [51




] [52] [53] [54] [55] [56] [57] [58

])
(text/Inside_Cover_Of_The_Text_Material_Complete.tex [59

]
Underfull \hbox (badness 10000) in paragraph at lines 181--182

 []


Overfull \hbox (8.29941pt too wide) in paragraph at lines 206--213
[][] 
 []


Underfull \hbox (badness 10000) in paragraph at lines 188--222
$[]$ $[]$
 []


Overfull \hbox (9.8515pt too wide) in paragraph at lines 233--240
[][] 
 []

[60

] [61

] [62

]
Underfull \hbox (badness 10000) in paragraph at lines 643--647

 []


Underfull \hbox (badness 10000) in paragraph at lines 653--659

 []

Requested font "cmr12" at 12.0pt
Requested font "cmmi12" at 12.0pt
Requested font "cmsy10" at 12.0pt
Requested font "cmex10" at 12.0pt
Requested font "msam10" at 12.0pt
Requested font "msbm10" at 12.0pt
Requested font "vect10" at 12.0pt
Requested font "[cmmi10]/OT:mapping=tex-text;" at 12.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
Requested font "[cmmi10]/I/OT:mapping=tex-text;" at 12.0pt
 -> C:/Program Files/MiKTeX 2.9/fonts/type1/public/amsfonts/cm/cmmi10.pfb
[63

])
Package atenddvi Info: Last page = 670.
 [64

]
Package atveryend Info: Empty hook `BeforeClearDocument' on input line 255.
Package atveryend Info: Executing hook `AfterLastShipout' on input line 255.
 (Math1010text.aux)
Package atveryend Info: Empty hook `AtVeryEndDocument' on input line 255.
Package atveryend Info: Empty hook `AtEndAfterFileList' on input line 255.


LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.

Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 255.
 ) 
Here is how much of TeX's memory you used:
 58867 strings out of 428755
 1259997 string characters out of 3164219
 1563901 words of memory out of 3000000
 57534 multiletter control sequences out of 15000+200000
 19712 words of font info for 151 fonts, out of 3000000 for 9000
 1096 hyphenation exceptions out of 8191
 62i,30n,91p,10385b,1071s stack positions out of 5000i,500n,10000p,200000b,50000s

Output written on Math1010text.pdf (670 pages).