Homework 2.log

This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex 2015.5.24)  29 SEP 2017 11:42
entering extended mode
 restricted \write18 enabled.
 %&-line parsing enabled.
**"Homework 2.tex"
(./Homework 2.tex
LaTeX2e <2015/01/01>
Babel <3.9l> and hyphenation patterns for 79 languages loaded.
(/usr/local/texlive/2015/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/local/texlive/2015/texmf-dist/tex/latex/base/size11.clo
File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
)
\c@part=\count79
\c@section=\count80
\c@subsection=\count81
\c@subsubsection=\count82
\c@paragraph=\count83
\c@subparagraph=\count84
\c@figure=\count85
\c@table=\count86
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/base/fontenc.sty
Package: fontenc 2005/09/27 v1.99g Standard LaTeX package

(/usr/local/texlive/2015/texmf-dist/tex/latex/base/t1enc.def
File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file
LaTeX Font Info:    Redeclaring font encoding T1 on input line 48.
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/psnfss/palatino.sty
Package: palatino 2005/04/12 PSNFSS-v9.2a (SPQR) 
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/graphics/graphicx.sty
Package: graphicx 2014/10/28 v1.0g Enhanced LaTeX Graphics (DPC,SPQR)

(/usr/local/texlive/2015/texmf-dist/tex/latex/graphics/keyval.sty
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
\KV@toks@=\toks14
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/graphics/graphics.sty
Package: graphics 2014/10/28 v1.0p Standard LaTeX Graphics (DPC,SPQR)

(/usr/local/texlive/2015/texmf-dist/tex/latex/graphics/trig.sty
Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/latexconfig/graphics.cfg
File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live
)
Package graphics Info: Driver file: pdftex.def on input line 94.

(/usr/local/texlive/2015/texmf-dist/tex/latex/pdftex-def/pdftex.def
File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX

(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/infwarerr.sty
Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO)
)
(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/ltxcmds.sty
Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO)
)
\Gread@gobject=\count87
))
\Gin@req@height=\dimen103
\Gin@req@width=\dimen104
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/caption/caption.sty
Package: caption 2013/05/02 v3.3-89 Customizing captions (AR)

(/usr/local/texlive/2015/texmf-dist/tex/latex/caption/caption3.sty
Package: caption3 2013/05/02 v1.6-88 caption3 kernel (AR)
Package caption3 Info: TeX engine: e-TeX on input line 57.
\captionmargin=\dimen105
\captionmargin@=\dimen106
\captionwidth=\dimen107
\caption@tempdima=\dimen108
\caption@indent=\dimen109
\caption@parindent=\dimen110
\caption@hangindent=\dimen111
)
\c@ContinuedFloat=\count88
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/adjustbox/adjustbox.sty
Package: adjustbox 2012/05/21 v1.0 Adjusting TeX boxes (trim, clip, ...)

(/usr/local/texlive/2015/texmf-dist/tex/latex/xkeyval/xkeyval.sty
Package: xkeyval 2014/12/03 v2.7a package option processing (HA)

(/usr/local/texlive/2015/texmf-dist/tex/generic/xkeyval/xkeyval.tex
(/usr/local/texlive/2015/texmf-dist/tex/generic/xkeyval/xkvutils.tex
\XKV@toks=\toks15
\XKV@tempa@toks=\toks16
)
\XKV@depth=\count89
File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA)
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/adjustbox/adjcalc.sty
Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back
-ends (calc, etex, pgfmath)
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/adjustbox/trimclip.sty
Package: trimclip 2012/05/16 v1.0 Trim and clip general TeX material

(/usr/local/texlive/2015/texmf-dist/tex/latex/collectbox/collectbox.sty
Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes
\collectedbox=\box26
)
\tc@llx=\dimen112
\tc@lly=\dimen113
\tc@urx=\dimen114
\tc@ury=\dimen115
Package trimclip Info: Using driver 'tc-pdftex.def'.

(/usr/local/texlive/2015/texmf-dist/tex/latex/adjustbox/tc-pdftex.def
File: tc-pdftex.def 2012/05/13 v1.0 Clipping driver for pdftex
))
\adjbox@Width=\dimen116
\adjbox@Height=\dimen117
\adjbox@Depth=\dimen118
\adjbox@Totalheight=\dimen119

(/usr/local/texlive/2015/texmf-dist/tex/latex/ifoddpage/ifoddpage.sty
Package: ifoddpage 2011/09/13 v1.0 Conditionals for odd/even page detection
\c@checkoddpage=\count90
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/varwidth/varwidth.sty
Package: varwidth 2009/03/30 ver 0.92;  Variable-width minipages
\@vwid@box=\box27
\sift@deathcycles=\count91
\@vwid@loff=\dimen120
\@vwid@roff=\dimen121
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/xcolor/xcolor.sty
Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK)

(/usr/local/texlive/2015/texmf-dist/tex/latex/latexconfig/color.cfg
File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive
)
Package xcolor Info: Driver file: pdftex.def on input line 225.
Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337.
Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1341.
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.
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/tools/enumerate.sty
Package: enumerate 2014/10/28 v3.00 enumerate extensions (DPC)
\@enLab=\toks17
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/geometry/geometry.sty
Package: geometry 2010/09/12 v5.6 Page Geometry

(/usr/local/texlive/2015/texmf-dist/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 detected.
)
(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/ifvtex.sty
Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO)
Package ifvtex Info: VTeX not detected.
)
(/usr/local/texlive/2015/texmf-dist/tex/generic/ifxetex/ifxetex.sty
Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
)
\Gm@cnth=\count92
\Gm@cntv=\count93
\c@Gm@tempcnt=\count94
\Gm@bindingoffset=\dimen122
\Gm@wd@mp=\dimen123
\Gm@odd@mp=\dimen124
\Gm@even@mp=\dimen125
\Gm@layoutwidth=\dimen126
\Gm@layoutheight=\dimen127
\Gm@layouthoffset=\dimen128
\Gm@layoutvoffset=\dimen129
\Gm@dimlist=\toks18
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/amsmath/amsmath.sty
Package: amsmath 2013/01/14 v2.14 AMS math features
\@mathmargin=\skip43

For additional information on amsmath, use the `?' option.
(/usr/local/texlive/2015/texmf-dist/tex/latex/amsmath/amstext.sty
Package: amstext 2000/06/29 v2.01

(/usr/local/texlive/2015/texmf-dist/tex/latex/amsmath/amsgen.sty
File: amsgen.sty 1999/11/30 v2.0
\@emptytoks=\toks19
\ex@=\dimen130
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/amsmath/amsbsy.sty
Package: amsbsy 1999/11/29 v1.2d
\pmbraise@=\dimen131
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/amsmath/amsopn.sty
Package: amsopn 1999/12/14 v2.01 operator names
)
\inf@bad=\count95
LaTeX Info: Redefining \frac on input line 210.
\uproot@=\count96
\leftroot@=\count97
LaTeX Info: Redefining \overline on input line 306.
\classnum@=\count98
\DOTSCASE@=\count99
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@=\box28
\strutbox@=\box29
\big@size=\dimen132
LaTeX Font Info:    Redeclaring font encoding OML on input line 566.
LaTeX Font Info:    Redeclaring font encoding OMS on input line 567.
\macc@depth=\count100
\c@MaxMatrixCols=\count101
\dotsspace@=\muskip10
\c@parentequation=\count102
\dspbrk@lvl=\count103
\tag@help=\toks20
\row@=\count104
\column@=\count105
\maxfields@=\count106
\andhelp@=\toks21
\eqnshift@=\dimen133
\alignsep@=\dimen134
\tagshift@=\dimen135
\tagwidth@=\dimen136
\totwidth@=\dimen137
\lineht@=\dimen138
\@envbody=\toks22
\multlinegap=\skip44
\multlinetaggap=\skip45
\mathdisplay@stack=\toks23
LaTeX Info: Redefining \[ on input line 2665.
LaTeX Info: Redefining \] on input line 2666.
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2013/01/14 v3.01 AMS font symbols

(/usr/local/texlive/2015/texmf-dist/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.
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/base/textcomp.sty
Package: textcomp 2005/09/27 v1.99g Standard LaTeX package
Package textcomp Info: Sub-encoding information:
(textcomp)               5 = only ISO-Adobe without \textcurrency
(textcomp)               4 = 5 + \texteuro
(textcomp)               3 = 4 + \textohm
(textcomp)               2 = 3 + \textestimated + \textcurrency
(textcomp)               1 = TS1 - \textcircled - \t
(textcomp)               0 = TS1 (full)
(textcomp)             Font families with sub-encoding setting implement
(textcomp)             only a restricted character set as indicated.
(textcomp)             Family '?' is the default used for unknown fonts.
(textcomp)             See the documentation for details.
Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 79.

(/usr/local/texlive/2015/texmf-dist/tex/latex/base/ts1enc.def
File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file
)
LaTeX Info: Redefining \oldstylenums on input line 334.
Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 349.
Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 350.
Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 351.
Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 352.
Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 353.
Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 354.
Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 355.
Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 356.
Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 357.
Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 358.
Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 359.
Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 360.
Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 361.
Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 362.
Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 363.
Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 364.
Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 365.
Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 366.
Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 367.
Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 368.
Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 369.
Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 370.
Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 371.
Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 372.

Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 373.
Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 374.
Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 375.
Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 376.
Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 377.
Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 378.
Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 379.
Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 380.
Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 381.
Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 382.
Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 383.
Package textcomp Info: Setting lmtt sub-encoding to TS1/0 on input line 384.
Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 385.
Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 386.
Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 387.
Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 388.
Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 389.
Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 390.
Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 391.
Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 392.
Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 393.
Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 394.
Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 395.
Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 396.
Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 397.
Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 398.
Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 399.
Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 400.
Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 401.
Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 402.
Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 403.
Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 404.
Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 405.
Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 406.
Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 407.
Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 408.
Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 409.
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/upquote/upquote.sty
Package: upquote 2012/04/19 v1.3 upright-quote and grave-accent glyphs in verba
tim
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/eurosym/eurosym.sty
Package: eurosym 1998/08/06 v1.1 European currency symbol ``Euro''
\@eurobox=\box30
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/ucs/ucs.sty
Package: ucs 2013/05/11 v2.2 UCS: Unicode input support

(/usr/local/texlive/2015/texmf-dist/tex/latex/ucs/data/uni-global.def
File: uni-global.def 2013/05/13 UCS: Unicode global data
)
\uc@secondtry=\count107
\uc@combtoks=\toks24
\uc@combtoksb=\toks25
\uc@temptokena=\toks26
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/base/inputenc.sty
Package: inputenc 2015/03/17 v1.2c Input encoding file
\inpenc@prehook=\toks27
\inpenc@posthook=\toks28

(/usr/local/texlive/2015/texmf-dist/tex/latex/ucs/utf8x.def
File: utf8x.def 2004/10/17 UCS: Input encoding UTF-8
))
(/usr/local/texlive/2015/texmf-dist/tex/latex/fancyvrb/fancyvrb.sty
Package: fancyvrb 2008/02/07

Style option: `fancyvrb' v2.7a, with DG/SPQR fixes, and firstline=lastline fix 
<2008/02/07> (tvz)
\FV@CodeLineNo=\count108
\FV@InFile=\read1
\FV@TabBox=\box31
\c@FancyVerbLine=\count109
\FV@StepNumber=\count110
\FV@OutFile=\write3
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/grffile.sty
Package: grffile 2012/04/05 v1.16 Extended file name support for graphics (HO)

(/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/kvoptions.sty
Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO)

(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty
Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO)

(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/etexcmds.sty
Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)

(/usr/local/texlive/2015/texmf-dist/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.
)))
(/usr/local/texlive/2015/texmf-dist/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: \pdf@primitive is available.
Package pdftexcmds Info: \pdf@ifprimitive is available.
Package pdftexcmds Info: \pdfdraftmode found.
)
Package grffile Info: Option `multidot' is set to `true'.
Package grffile Info: Option `extendedchars' is set to `false'.
Package grffile Info: Option `space' is set to `true'.
Package grffile Info: \Gin@ii of package `graphicx' fixed on input line 486.
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/hyperref/hyperref.sty
Package: hyperref 2012/11/06 v6.83m Hypertext links for LaTeX

(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
Package: hobsub-hyperref 2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO)


(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty
Package: hobsub-generic 2012/05/28 v1.13 Bundle oberdiek, subset generic (HO)
Package: hobsub 2012/05/28 v1.13 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: kvdefinekeys 2011/04/07 v1.3 Define keys (HO)
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 2012/05/28 v1.2 Wrapper for package hooks (HO)
Package: xcolor-patch 2011/01/30 xcolor patch
Package: atveryend 2011/06/30 v1.8 Hooks at the very end of document (HO)
Package atveryend Info: \enddocument detected (standard20110627).
Package: atbegshi 2011/10/05 v1.16 At begin shipout hook (HO)
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)
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/auxhook.sty
Package: auxhook 2011/03/04 v1.3 Hooks for auxiliary files (HO)
)
\@linkdim=\dimen139
\Hy@linkcounter=\count111
\Hy@pagecounter=\count112

(/usr/local/texlive/2015/texmf-dist/tex/latex/hyperref/pd1enc.def
File: pd1enc.def 2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO)
)
\Hy@SavedSpaceFactor=\count113

(/usr/local/texlive/2015/texmf-dist/tex/latex/latexconfig/hyperref.cfg
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
)
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=\count114

(/usr/local/texlive/2015/texmf-dist/tex/latex/url/url.sty
\Urlmuskip=\muskip11
Package: url 2013/09/16  ver 3.4  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 5041.
\XeTeXLinkMargin=\dimen140
\Fld@menulength=\count115
\Field@Width=\dimen141
\Fld@charsize=\dimen142
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=\count116
\c@Item=\count117
\c@Hfootnote=\count118
)

Package hyperref Message: Driver (autodetected): hpdftex.

(/usr/local/texlive/2015/texmf-dist/tex/latex/hyperref/hpdftex.def
File: hpdftex.def 2012/11/06 v6.83m Hyperref driver for pdfTeX
\Fld@listcount=\count119
\c@bookmark@seq@number=\count120

(/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty
Package: rerunfilecheck 2011/04/15 v1.7 Rerun checks for auxiliary files (HO)
Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2
82.
)
\Hy@SectionHShift=\skip46
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/tools/longtable.sty
Package: longtable 2014/10/28 v4.11 Multi-page Table package (DPC)
\LTleft=\skip47
\LTright=\skip48
\LTpre=\skip49
\LTpost=\skip50
\LTchunksize=\count121
\LTcapwidth=\dimen143
\LT@head=\box32
\LT@firsthead=\box33
\LT@foot=\box34
\LT@lastfoot=\box35
\LT@cols=\count122
\LT@rows=\count123
\c@LT@tables=\count124
\c@LT@chunks=\count125
\LT@p@ftn=\toks29
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/booktabs/booktabs.sty
Package: booktabs 2005/04/14 v1.61803 publication quality tables
\heavyrulewidth=\dimen144
\lightrulewidth=\dimen145
\cmidrulewidth=\dimen146
\belowrulesep=\dimen147
\belowbottomsep=\dimen148
\aboverulesep=\dimen149
\abovetopsep=\dimen150
\cmidrulesep=\dimen151
\cmidrulekern=\dimen152
\defaultaddspace=\dimen153
\@cmidla=\count126
\@cmidlb=\count127
\@aboverulesep=\dimen154
\@belowrulesep=\dimen155
\@thisruleclass=\count128
\@lastruleclass=\count129
\@thisrulewidth=\dimen156
)
(/usr/local/texlive/2015/texmf-dist/tex/generic/ulem/ulem.sty
\UL@box=\box36
\UL@hyphenbox=\box37
\UL@skip=\skip51
\UL@hook=\toks30
\UL@height=\dimen157
\UL@pe=\count130
\UL@pixel=\dimen158
\ULC@box=\box38
Package: ulem 2012/05/18
\ULdepth=\dimen159
)
(/usr/local/texlive/2015/texmf-dist/tex/latex/setspace/setspace.sty
Package: setspace 2011/12/19 v6.7a set line spacing
)
Package hyperref Info: Option `breaklinks' set `true' on input line 264.
Package hyperref Info: Option `colorlinks' set `true' on input line 264.

(./Homework 2.aux)
\openout1 = `"Homework 2.aux"'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 271.
LaTeX Font Info:    Try loading font information for TS1+cmr on input line 271.

 (/usr/local/texlive/2015/texmf-dist/tex/latex/base/ts1cmr.fd
File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions
)
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 271.
LaTeX Font Info:    ... okay on input line 271.
LaTeX Font Info:    Try loading font information for T1+ppl on input line 271.
 (/usr/local/texlive/2015/texmf-dist/tex/latex/psnfss/t1ppl.fd
File: t1ppl.fd 2001/06/04 font definitions for T1/ppl.
)
(/usr/local/texlive/2015/texmf-dist/tex/context/base/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
\scratchcounter=\count131
\scratchdimen=\dimen160
\scratchbox=\box39
\nofMPsegments=\count132
\nofMParguments=\count133
\everyMPshowfont=\toks31
\MPscratchCnt=\count134
\MPscratchDim=\dimen161
\MPnumerator=\count135
\makeMPintoPDFobject=\count136
\everyMPtoPDFconversion=\toks32
) (/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf

(/usr/local/texlive/2015/texmf-dist/tex/latex/oberdiek/grfext.sty
Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO)
)
Package grfext Info: Graphics extension search list:
(grfext)             [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE
G,.JBIG2,.JB2,.eps]
(grfext)             \AppendGraphicsExtensions on input line 452.

(/usr/local/texlive/2015/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
e
))
Package caption Info: Begin \AtBeginDocument code.
Package caption Info: hyperref package is loaded.
Package caption Info: longtable package is loaded.

(/usr/local/texlive/2015/texmf-dist/tex/latex/caption/ltcaption.sty
Package: ltcaption 2013/02/03 v1.3-62 longtable captions (AR)
)
Package caption Info: End \AtBeginDocument code.

*geometry* driver: auto-detecting
*geometry* detected driver: pdftex

Package geometry Warning: The marginal notes overrun the paper.
     Add 32.865pt and more to the right margin.

*geometry* verbose mode - [ preamble ] result:
* driver: pdftex
* paper: <default>
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: 
* h-part:(L,W,R)=(54.2025pt, 523.9575pt, 36.135pt)
* v-part:(T,H,B)=(54.2025pt, 704.63249pt, 36.135pt)
* \paperwidth=614.295pt
* \paperheight=794.96999pt
* \textwidth=523.9575pt
* \textheight=704.63249pt
* \oddsidemargin=-18.06749pt
* \evensidemargin=-18.06749pt
* \topmargin=-55.06749pt
* \headheight=12.0pt
* \headsep=25.0pt
* \topskip=11.0pt
* \footskip=30.0pt
* \marginparwidth=59.0pt
* \marginparsep=10.0pt
* \columnsep=10.0pt
* \skip\footins=10.0pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidefalse
* \@mparswitchfalse
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

(/usr/local/texlive/2015/texmf-dist/tex/latex/ucs/ucsencs.def
File: ucsencs.def 2011/01/21 Fixes to fontencodings LGR, T3
)
\AtBeginShipoutBox=\box40
Package hyperref Info: Link coloring ON on input line 271.

(/usr/local/texlive/2015/texmf-dist/tex/latex/hyperref/nameref.sty
Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section

(/usr/local/texlive/2015/texmf-dist/tex/generic/oberdiek/gettitlestring.sty
Package: gettitlestring 2010/12/03 v1.4 Cleanup title references (HO)
)
\c@section@level=\count137
)
LaTeX Info: Redefining \ref on input line 271.
LaTeX Info: Redefining \pageref on input line 271.
LaTeX Info: Redefining \nameref on input line 271.

(./Homework 2.out) (./Homework 2.out)
\@outlinefile=\write4
\openout4 = `"Homework 2.out"'.

 (../title.tex
<"/Users/Braden/Documents/College/Latex/logo".png, id=96, 138.46931pt x 119.390
05pt>
File: "/Users/Braden/Documents/College/Latex/logo".png Graphic file (type png)
 <use "/Users/Braden/Documents/College/Latex/logo".png>
Package pdftex.def Info: "/Users/Braden/Documents/College/Latex/logo".png used 
on input line 10.
(pdftex.def)             Requested size: 110.7756pt x 95.51215pt.
LaTeX Font Info:    Font shape `T1/ppl/bx/n' in size <14.4> not available
(Font)              Font shape `T1/ppl/b/n' tried instead on input line 17.
 [1

{/usr/local/texlive/2015/texmf-var/fonts/map/pdftex/updmap/pdftex.map} </Users/
Braden/Documents/College/Latex/logo.png>])
LaTeX Font Info:    Font shape `T1/ppl/bx/n' in size <12> not available
(Font)              Font shape `T1/ppl/b/n' tried instead on input line 281.
LaTeX Font Info:    Try loading font information for U+msa on input line 289.

(/usr/local/texlive/2015/texmf-dist/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
)
LaTeX Font Info:    Try loading font information for U+msb on input line 289.

(/usr/local/texlive/2015/texmf-dist/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
)
LaTeX Font Info:    Font shape `T1/ppl/bx/n' in size <10.95> not available
(Font)              Font shape `T1/ppl/b/n' tried instead on input line 293.
pdfTeX warning (ext4): destination with the same identifier (name{page.1}) has 
been already used, duplicate ignored
<to be read again> 
                   \relax 
l.357 \end{align}
                  [1]
<interpolation_example.png, id=111, 770.88pt x 519.9425pt>
File: interpolation_example.png Graphic file (type png)

<use interpolation_example.png>
Package pdftex.def Info: interpolation_example.png used on input line 378.
(pdftex.def)             Requested size: 419.16759pt x 282.71646pt.
 [2 <./interpolation_example.png>]
<rssY.png, id=125, 436.63126pt x 402.50375pt>
File: rssY.png Graphic file (type png)
 <use rssY.png>
Package pdftex.def Info: rssY.png used on input line 419.
(pdftex.def)             Requested size: 349.30548pt x 322.00343pt.

Underfull \hbox (badness 3098) in paragraph at lines 418--420
[]\T1/ppl/m/n/10.95 Therefore the line y = $[]$ min-i-mizes the RSS in the y ax
is as shown by the im-age be-low:
 []

[3 <./rssY.png>]
LaTeX Font Info:    Try loading font information for T1+pcr on input line 446.
 (/usr/local/texlive/2015/texmf-dist/tex/latex/psnfss/t1pcr.fd
File: t1pcr.fd 2001/06/04 font definitions for T1/pcr.
)
LaTeX Font Info:    Font shape `T1/pcr/bx/n' in size <10.95> not available
(Font)              Font shape `T1/pcr/b/n' tried instead on input line 447.
LaTeX Font Info:    Try loading font information for TS1+pcr on input line 452.

(/usr/local/texlive/2015/texmf-dist/tex/latex/psnfss/ts1pcr.fd
File: ts1pcr.fd 2001/06/04 font definitions for TS1/pcr.
)
<Homework 2_files/Homework 2_23_1.png, id=131, 773.89125pt x 519.9425pt>
File: Homework 2_files/Homework 2_23_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_23_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_23_1.png used on input lin
e 493.
(pdftex.def)             Requested size: 773.88936pt x 519.94124pt.

Underfull \hbox (badness 10000) in paragraph at lines 495--496

 []

[4 <./Homework 2_files/Homework 2_23_1.png>]
LaTeX Font Info:    Font shape `T1/pcr/m/it' in size <10.95> not available
(Font)              Font shape `T1/pcr/m/sl' tried instead on input line 512.
 [5]
<Homework 2_files/Homework 2_30_0.png, id=144, 773.89125pt x 540.0175pt>
File: Homework 2_files/Homework 2_30_0.png Graphic file (type png)

<use Homework 2_files/Homework 2_30_0.png>
Package pdftex.def Info: Homework 2_files/Homework 2_30_0.png used on input lin
e 594.
(pdftex.def)             Requested size: 773.88936pt x 540.01617pt.

Underfull \hbox (badness 10000) in paragraph at lines 596--597

 []

[6 <./Homework 2_files/Homework 2_30_0.png>] [7]
<Homework 2_files/Homework 2_31_1.png, id=155, 761.84625pt x 593.21625pt>
File: Homework 2_files/Homework 2_31_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_31_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_31_1.png used on input lin
e 670.
(pdftex.def)             Requested size: 761.84439pt x 593.2148pt.

Underfull \hbox (badness 10000) in paragraph at lines 672--673

 []

[8 <./Homework 2_files/Homework 2_31_1.png>]
<Homework 2_files/Homework 2_33_1.png, id=161, 1899.095pt x 1772.6225pt>
File: Homework 2_files/Homework 2_33_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_33_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_33_1.png used on input lin
e 711.
(pdftex.def)             Requested size: 1899.09038pt x 1772.6182pt.
 [9]
Underfull \hbox (badness 10000) in paragraph at lines 713--714

 []

[10 <./Homework 2_files/Homework 2_33_1.png>]
<Homework 2_files/Homework 2_41_1.png, id=172, 1506.62875pt x 1411.2725pt>
File: Homework 2_files/Homework 2_41_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_41_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_41_1.png used on input lin
e 810.
(pdftex.def)             Requested size: 1506.62508pt x 1411.26907pt.
 [11]
Underfull \hbox (badness 10000) in paragraph at lines 812--813

 []

<Homework 2_files/Homework 2_42_1.png, id=177, 795.97375pt x 600.2425pt>
File: Homework 2_files/Homework 2_42_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_42_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_42_1.png used on input lin
e 825.
(pdftex.def)             Requested size: 795.97182pt x 600.24103pt.
 [12 <./Homework 2_files/Homework 2_41_1.png>]
Underfull \hbox (badness 10000) in paragraph at lines 827--828

 []

[13 <./Homework 2_files/Homework 2_42_1.png>]
<Homework 2_files/Homework 2_46_1.png, id=189, 768.8725pt x 540.0175pt>
File: Homework 2_files/Homework 2_46_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_46_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_46_1.png used on input lin
e 909.
(pdftex.def)             Requested size: 768.87062pt x 540.01617pt.
 [14]
Underfull \hbox (badness 10000) in paragraph at lines 911--912

 []

<Homework 2_files/Homework 2_47_1.png, id=194, 738.76pt x 562.1pt>
File: Homework 2_files/Homework 2_47_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_47_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_47_1.png used on input lin
e 927.
(pdftex.def)             Requested size: 738.75818pt x 562.09863pt.
 [15 <./Homework 2_files/Homework 2_46_1.png>]
Underfull \hbox (badness 10000) in paragraph at lines 929--930

 []

<Homework 2_files/Homework 2_51_1.png, id=200, 738.76pt x 542.025pt>
File: Homework 2_files/Homework 2_51_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_51_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_51_1.png used on input lin
e 965.
(pdftex.def)             Requested size: 738.75818pt x 542.02367pt.
 [16 <./Homework 2_files/Homework 2_47_1.png>]
Underfull \hbox (badness 10000) in paragraph at lines 967--968

 []

[17 <./Homework 2_files/Homework 2_51_1.png>]
<Homework 2_files/Homework 2_56_1.png, id=211, 740.7675pt x 542.025pt>
File: Homework 2_files/Homework 2_56_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_56_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_56_1.png used on input lin
e 1043.
(pdftex.def)             Requested size: 740.76569pt x 542.02367pt.
 [18]
Underfull \hbox (badness 10000) in paragraph at lines 1045--1046

 []

[19 <./Homework 2_files/Homework 2_56_1.png>] [20] [21] [22]
<Homework 2_files/Homework 2_71_1.png, id=234, 735.74875pt x 542.025pt>
File: Homework 2_files/Homework 2_71_1.png Graphic file (type png)

<use Homework 2_files/Homework 2_71_1.png>
Package pdftex.def Info: Homework 2_files/Homework 2_71_1.png used on input lin
e 1291.
(pdftex.def)             Requested size: 735.74695pt x 542.02367pt.

Underfull \hbox (badness 10000) in paragraph at lines 1293--1294

 []

[23 <./Homework 2_files/Homework 2_71_1.png>]
Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1329.
 [24]
Package atveryend Info: Empty hook `AfterLastShipout' on input line 1329.
 (./Homework 2.aux)
Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1329.
Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 1329.

Package rerunfilecheck Info: File `"Homework 2".out' has not changed.
(rerunfilecheck)             Checksum: E45C9CEB3D9BA1B3210C05CF6DD6C2BE;1665.
Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 1329.
 ) 
Here is how much of TeX's memory you used:
 10634 strings out of 493089
 160458 string characters out of 6134842
 264438 words of memory out of 5000000
 13852 multiletter control sequences out of 15000+600000
 26031 words of font info for 58 fonts, out of 8000000 for 9000
 1141 hyphenation exceptions out of 8191
 36i,8n,38p,598b,461s stack positions out of 5000i,500n,10000p,200000b,80000s
{/usr/local/texlive/2015/texmf-dist/fonts/enc/dvips/base/8r.enc}</usr/local/t
exlive/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/te
xlive/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/local/texl
ive/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive
/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/texlive/
2015/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/local/texl
ive/2015/texmf-dist/fonts/type1/urw/courier/ucrb8a.pfb></usr/local/texlive/2015
/texmf-dist/fonts/type1/urw/courier/ucrr8a.pfb></usr/local/texlive/2015/texmf-d
ist/fonts/type1/urw/courier/ucrro8a.pfb></usr/local/texlive/2015/texmf-dist/fon
ts/type1/urw/palatino/uplb8a.pfb></usr/local/texlive/2015/texmf-dist/fonts/type
1/urw/palatino/uplr8a.pfb>
Output written on "Homework 2.pdf" (25 pages, 1630062 bytes).
PDF statistics:
 294 PDF objects out of 1000 (max. 8388607)
 226 compressed objects within 3 object streams
 53 named destinations out of 1000 (max. 500000)
 255 words of extra memory for PDF output out of 10000 (max. 10000000)