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'mm' on line 540. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \newAATfeature with sig. 'mmmm' on line 548. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \newopentypefeature with sig. 'mmm' on line 556. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \aliasfontfeature with sig. 'mm' on line 577. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \aliasfontfeatureoption with sig. 'mmm' on line 586. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \newfontscript with sig. 'mm' on line 590. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \newfontlanguage with sig. 'mm' on line 594. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareFontsExtensions with sig. 'm' on line 599. +................................................. +\l__fontspec_tmp_int=\count131 + +(/usr/local/texlive/2015/texmf-dist/tex/latex/fontspec/fontspec.cfg) +LaTeX Info: Redefining \itshape on input line 2705. +LaTeX Info: Redefining \slshape on input line 2710. +LaTeX Info: Redefining \scshape on input line 2715. +LaTeX Info: Redefining \upshape on input line 2720. +\l__fontspec_em_int=\count132 +\l__fontspec_emdef_int=\count133 +LaTeX Info: Redefining \em on input line 2736. +LaTeX Info: Redefining \emph on input line 2742. +LaTeX Info: Redefining \- on input line 2746. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \oldstylenums with sig. 'm' on line 2841. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \liningnums with sig. 'm' on line 2845. +................................................. +)) +(/usr/local/texlive/2015/texmf-dist/tex/xelatex/xecjk/xunicode-addon.sty +Package: xunicode-addon 2016/02/10 v3.3.4 addon file for xunicode +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \ReloadXunicode with sig. 'm' on line 87. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \DeclareUTFmathsymbols with sig. 'm' on line 132. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \UseMathAsText with sig. '' on line 141. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \UndeclareUTFcharacter with sig. 'O{\UTFencname }mm' on +. line 176. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \UndeclareUTFcomposite with sig. 'O{\UTFencname }mmm' on +. line 183. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \DeclareUTFcharacter with sig. 'O{\UTFencname }mm' on +. line 210. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFSymbol with sig. 'mO{\UTFencname }m' on line +. 236. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFCommand with sig. 'mO{\UTFencname }m' on line +. 238. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \DeclareUTFcomposite with sig. 'O{\UTFencname }mmm' on +. line 281. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFCompositeCommand with sig. 'mO{\UTFencname }mm' +. on line 294. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFCompositeSymbol with sig. 'mO{\UTFencname }mm' +. on line 299. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFComposite with sig. 'mO{\UTFencname }' on line +. 301. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFEncodedAccent with sig. 'mO{\UTFencname }mm' on +. line 303. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFEncodedAccents with sig. 'mO{\UTFencname }mm' on +. line 305. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFEncodedSymbol with sig. 'mO{\UTFencname }mm' on +. line 307. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFEncodedCircle with sig. 'mO{\UTFencname }mm' on +. line 309. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \DeclareEncodedCompositeCharacter with sig. 'mmmm' on +. line 311. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \DeclareEncodedCompositeAccents with sig. 'mmmm' on line +. 313. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFDoubleEncodedAccent with sig. 'mO{\UTFencname +. }mm' on line 315. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFDoubleEncodedSymbol with sig. 'mO{\UTFencname +. }mm' on line 317. +................................................. +\l__xunadd_tmp_coffin=\box43 +\l__xunadd_circle_coffin=\box44 +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \settextcircledratio with sig. 'm' on line 468. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \AtBeginUTFCommand with sig. 'sO{}+m' on line 537. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \AtEndUTFCommand with sig. 'sO{}+m' on line 547. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \DeclareUTFTIPACommand with sig. 'O{\UTFencname }m' on line +. 579. +................................................. +) +(/usr/local/texlive/2015/texmf-dist/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 + +*** Reloading Xunicode for encoding 'EU1' *** +) (/usr/local/texlive/2015/texmf-dist/tex/xelatex/xecjk/xunicode-extra.def +File: xunicode-extra.def 2016/02/10 v3.3.4 extra definition for xunicode +) +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKsetup with sig. '+m' on line 3588. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKsetemboldenfactor with sig. 'm' on line 3590. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKsetslantfactor with sig. 'm' on line 3592. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \punctstyle with sig. 'm' on line 3593. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKplainchr with sig. '' on line 3594. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CJKsetecglue with sig. 'm' on line 3595. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CJKspace with sig. '' on line 3597. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CJKnospace with sig. '' on line 3598. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKallowbreakbetweenpuncts with sig. '' on line 3600. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKnobreakbetweenpuncts with sig. '' on line 3602. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKenablefallback with sig. '' on line 3604. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKdisablefallback with sig. '' on line 3606. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKsetcharclass with sig. 'mmm' on line 3611. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \nobreakspace with sig. '' on line 3730. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \fontfamily with sig. 'm' on line 3776. +................................................. + +(/usr/local/texlive/2015/texmf-dist/tex/xelatex/xecjk/xeCJK.cfg +File: xeCJK.cfg 2016/02/10 v3.3.4 Configuration file for xeCJK package +)) +(/usr/local/texlive/2015/texmf-dist/tex/xelatex/xecjk/xeCJKfntef.sty +Package: xeCJKfntef 2016/02/10 v3.3.4 xeCJK font effect + +(/usr/local/texlive/2015/texmf-dist/tex/generic/ulem/ulem.sty +\UL@box=\box45 +\UL@hyphenbox=\box46 +\UL@skip=\skip54 +\UL@hook=\toks18 +\UL@height=\dimen172 +\UL@pe=\count134 +\UL@pixel=\dimen173 +\ULC@box=\box47 +Package: ulem 2012/05/18 +\ULdepth=\dimen174 +) +(/usr/local/texlive/2015/texmf-dist/tex/latex/environ/environ.sty +Package: environ 2014/05/04 v0.3 A new way to define environments + +(/usr/local/texlive/2015/texmf-dist/tex/latex/trimspaces/trimspaces.sty +Package: trimspaces 2009/09/17 v1.1 Trim spaces around a token list +) +\@envbody=\toks19 +) +(/usr/local/texlive/2015/texmf-dist/tex/latex/cjk/texinput/CJKfntef.sty +Package: CJKfntef 2015/04/18 4.8.4 +\CJK@fntefSkip=\skip55 +\CJK@nest=\count135 +\CJK@fntefDimen=\dimen175 +\CJK@underdotBox=\box48 +\CJK@ULbox=\box49 +\CJK@underanyskip=\dimen176 +) +\l__xeCJK_space_skip=\skip56 +\c__xeCJK_ulem-left_node_dim=\dimen177 +\c__xeCJK_null_box=\box50 +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \xeCJKfntefon with sig. 'st-so' on line 590. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderline with sig. 'st-so' on line 609. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \varCJKunderline with sig. '' on line 611. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderwave with sig. 'st-so' on line 621. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderdblline with sig. 'st-so' on line 645. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKsout with sig. 'st-so' on line 664. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKxout with sig. 'st-so' on line 681. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderanyline with sig. 'st-somm' on line 702. +................................................. +\l__xeCJK_fntef_box=\box51 +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderanysymbol with sig. 'ommm' on line 874. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \CJKunderdot with sig. 'om' on line 883. +................................................. +\l__xeCJK_under_symbol_box=\box52 +................................................. +. LaTeX info: "xparse/redefine-environment" +. +. Redefining environment 'CJKfilltwosides' with sig. 'O{c}m' on line 977. +................................................. +\c__xeCJK_filll_skip=\skip57 +) +\ccwd=\dimen178 +\l__ctex_ccglue_skip=\skip58 +) +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTEXsetfont with sig. '' on line 404. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \ziju with sig. 'm' on line 476. +................................................. +\l__ctex_ziju_dim=\dimen179 +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTEXindent with sig. '' on line 517. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTEXnoindent with sig. '' on line 523. +................................................. + +(/usr/local/texlive/2015/texmf-dist/tex/latex/zhnumber/zhnumber.sty +Package: zhnumber 2016/02/02 v2.3 Typesetting numbers with Chinese glyphs +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnumber with sig. '+o+m' on line 45. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnumberwithoptions with sig. '+m+m' on line 52. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnum with sig. '+o+m' on line 106. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnumwithoptions with sig. '+m+m' on line 113. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhdigits with sig. '+s+o+m' on line 291. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhdigitswithoptions with sig. '+m+m+m' on line 298. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhdate with sig. '+s+m' on line 357. +................................................. +\l__zhnum_scale_int=\count136 +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnumExtendScaleMap with sig. '>{\TrimSpaces }+o+m' on +. line 467. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zhnumsetup with sig. '+m' on line 898. +................................................. + +(/usr/local/texlive/2015/texmf-dist/tex/latex/zhnumber/zhnumber-utf8.cfg +File: zhnumber-utf8.cfg 2016/02/02 v2.3 Chinese numerals with UTF8 encoding +)) +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTEXnumber with sig. 'mm' on line 538. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTEXdigits with sig. 'mm' on line 540. +................................................. + +(/usr/local/texlive/2015/texmf-dist/tex/latex/ctex/scheme/ctex-scheme-chinese.d +ef +File: ctex-scheme-chinese.def 2016/02/02 v2.3 Chinese scheme for generic (CTEX) + + (/usr/local/texlive/2015/texmf-dist/tex/latex/ctex/config/ctex-name-utf8.cfg +File: ctex-name-utf8.cfg 2016/02/02 v2.3 Caption with encoding UTF8 (CTEX) +)) (/usr/local/texlive/2015/texmf-dist/tex/latex/tools/indentfirst.sty +Package: indentfirst 1995/11/23 v1.03 Indent first paragraph (DPC) +) +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \zihao with sig. 'm' on line 619. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \CTeX with sig. '' on line 723. +................................................. + +(/usr/local/texlive/2015/texmf-dist/tex/latex/ctex/fontset/ctex-fontset-mac.def +File: ctex-fontset-mac.def 2016/02/02 v2.3 Mac OS X fonts definition (CTEX) +************************************************* +* fontspec warning: "script-not-exist" +* +* Font 'STSong' does not contain script 'CJK'. +************************************************* +\g__fontspec_family_STSong_int=\count137 +................................................. +. fontspec info: "no-font-shape" +. +. Could not resolve font STKaiti/B (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "no-font-shape" +. +. Could not resolve font STHeiti/I (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "no-font-shape" +. +. Could not resolve font STSong/BI (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "defining-font" +. +. Font family 'STSong(0)' created for font 'STSong' with options +. [Script={CJK},BoldFont={STHeiti},ItalicFont={STKaiti}]. +. +. This font family consists of the following NFSS series/shapes: +. - 'normal' (m/n) with NFSS spec.: <->"STSong/OT:" +. - 'small caps' (m/sc) with NFSS spec.: - 'bold' (bx/n) with NFSS spec.: +. <->"STHeiti/OT:" +. - 'bold small caps' (bx/sc) with NFSS spec.: - 'italic' (m/it) with NFSS +. spec.: <->"STKaiti/OT:" +. - 'italic small caps' (m/itsc) with NFSS spec.: +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \songti with sig. '' on line 44. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \heiti with sig. '' on line 45. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \fangsong with sig. '' on line 46. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \kaishu with sig. '' on line 47. +................................................. +)) (/usr/local/texlive/2015/texmf-dist/tex/latex/ctex/config/ctex.cfg +File: ctex.cfg 2016/02/02 v2.3 Configuration file (CTEX) +) +(/usr/local/texlive/2015/texmf-dist/tex/latex/xltxtra/xltxtra.sty +Package: xltxtra 2016/01/21 v0.6 Improvements for the "XeLaTeX" format + +(/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. +) +(/usr/local/texlive/2015/texmf-dist/tex/latex/realscripts/realscripts.sty +Package: realscripts 2016/02/13 v0.3d Access OpenType subscripts and superscrip +ts +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \fakesubscript with sig. 'm' on line 19. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \fakesuperscript with sig. 'm' on line 22. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \textsubscript with sig. 's' on line 25. +................................................. +................................................. +. LaTeX info: "xparse/redefine-command" +. +. Redefining command \textsuperscript with sig. 's' on line 28. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \realsubscript with sig. 'm' on line 45. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \realsuperscript with sig. 'm' on line 60. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \textsubsuperscript with sig. 'sO{l}mm' on line 138. +................................................. +................................................. +. LaTeX info: "xparse/define-command" +. +. Defining command \textsupersubscript with sig. 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Could not resolve font 楷體-繁 粗體/I (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "no-font-shape" +. +. Could not resolve font 楷體-繁/BI (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "no-font-shape" +. +. Could not resolve font 楷體-繁/I (it probably doesn't exist). +................................................. +................................................. +. fontspec info: "defining-font" +. +. Font family '楷體-繁(0)' created for font '楷體-繁' with options +. [Script={CJK},BoldFont={楷體-繁 粗體}]. +. +. 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demo/exam.pdf b/Demo/exam demo/exam.pdf new file mode 100644 index 0000000..e004ef9 Binary files /dev/null and b/Demo/exam demo/exam.pdf differ diff --git a/Demo/exam demo/exam.synctex.gz b/Demo/exam demo/exam.synctex.gz new file mode 100644 index 0000000..0a8ec9f Binary files /dev/null and b/Demo/exam demo/exam.synctex.gz differ diff --git a/Demo/exam demo/exam.tex b/Demo/exam demo/exam.tex new file mode 100644 index 0000000..79fa5c4 --- /dev/null +++ b/Demo/exam demo/exam.tex @@ -0,0 +1,55 @@ +\documentclass[12pt]{article} +\usepackage[left=3.5cm,right=3.5cm,top=2.5cm,bottom=2.5cm]{geometry} +\usepackage{ctex} +\usepackage{fontspec,xltxtra,xunicode} +\XeTeXlinebreaklocale "zh" +\XeTeXlinebreakskip = 0pt plus 1pt +\setCJKmainfont[BoldFont={楷體-繁 粗體}]{楷體-繁} +\usepackage{amsthm} +\usepackage{amsmath} +\begin{document} +\begin{center} +{\Large \textbf{Calculus Quiz 1}} +\end{center} + +\begin{flushright} +February 27, 2013\\ Time: 11:10-12:10\\ +Total Number of points = 105 +\end{flushright} + +\begin{enumerate} +\item (30 points) The disk $(x−3)^2 +y^2 \le 1$ is revolved about the $y$-axis to generate a solid shaped like a doughnut and called a $torus$. Find its volume by +\begin{enumerate} +\item (15 points) the washer method. +\item (15 points) the shell method. +\end{enumerate} +Hint: Coming across the integral $\int^a_{-a}\sqrt{a^2-y^2}dy$, use the change of variable $y = a\sin u$. +\begin{proof} +\begin{enumerate} +\item Refer to Figure 1, and then the volume of the torus is +\begin{align*} +\int^1_{-1}\pi \left [\left (3+\sqrt{1-y^2}\right )^2-\left (3-\sqrt{1-y^2}\right)^2\right]dy&=\pi \int^1_{-1}6\cdot2\sqrt{1-y^2}dy\\ +&=12\pi \int^1_{-1}\sqrt{1-y^2}dy\\ +&=12\pi\cdot\frac{\pi\cdot 1^2}{2}\\ +&=6\pi^2, +\end{align*} +since $\int^1_{-1}\sqrt{1-y^2}dy$ is half the area of the unit circle. +\end{enumerate} +\end{proof} +\item (15 points) Find the length of the curve: +\[ +x=\int^y_0\sqrt{\sec^4t-1}dt,\quad \frac{-\pi}{4}\le y \le \frac{\pi}{4} +\] + +\item (15 points) Find the area of the surface generated by revolving about the $y$-axis the curve: +\[ +y=\sqrt{2x-x^2},\quad \frac{1}{2}\le y \le \frac{3}{2} +\] + +\item (15 points) State and prove the fundamental theorem of Calculus part one. +\item (15 points) State and prove the fundamental theorem of Calculus part two. +\item (15 points) State and prove the Mean Value Theorem for derivatives. + + +\end{enumerate} +\end{document}