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Original file line number | Diff line number | Diff line change |
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% !TEX TS-program = XeLaTeX | ||
% !TEX program = XeLaTeX | ||
%\errorcontextlines 10000 | ||
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\RequirePackage[l2tabu, orthodox]{nag} | ||
\documentclass[10pt]{book} | ||
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\input{headers/APEX_format} | ||
\usepackage{headers/apex_style} | ||
\input{headers/Header_Calculus} | ||
% this is not standalone | ||
% this is latexmlAlts to test if we need alternative latexml commands | ||
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\newcommand{\thetitle}{Standalone} | ||
\documentclass[10pt]{book} | ||
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\printallanswers | ||
\printincolor | ||
\usetwoDgraphics | ||
%\usethreeDgraphics | ||
%\input{headers/APEX_format} | ||
%\usepackage{headers/apex_style} | ||
%\input{headers/Header_Calculus} | ||
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% LaTeXML's hyperref overwrites these | ||
\newcommand{\chapterautorefname}{Chap\-ter} % the default is lowercase | ||
\newcommand{\sectionautorefname}{Sec\-tion} % the default is lowercase | ||
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\usepackage[marginparwidth=150pt]{geometry} | ||
\usepackage{amsmath} | ||
\usepackage{graphicx} | ||
\usepackage{tikz} | ||
\usepackage{enumitem} | ||
\usepackage{multicol} | ||
\usepackage{multirow} | ||
\usepackage{hyperref} | ||
\newlist{sectionexercises}{enumerate}{1} | ||
\newcounter{saveexercisenum}[section] | ||
\setlist[sectionexercises]{ | ||
label=\arabic*., | ||
ref=\arabic*, % ref overrides label | ||
before=\setcounter{sectionexercisesi}{\value{saveexercisenum}}, | ||
after=\setcounter{saveexercisenum}{\value{sectionexercisesi}}, | ||
} | ||
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\begin{document} | ||
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%\frontmatter | ||
% | ||
%\input{text/front_matter_and_cover} | ||
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\mainmatter | ||
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\setcounter{chapter}{4} | ||
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\setcounter{section}{2} | ||
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%\apexchapter[text/01_Prerequisite]{Limits}{ch:label} | ||
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%This chapter introduces \textbf{sequences} and \textbf{series}, important mathematical constructions that are useful when solving a large variety of mathematical problems. The content of this chapter is considerably different from the content of the chapters before it. While the material we learn here definitely falls under the scope of ``calculus,'' we will make very little use of derivatives or integrals. Limits are extremely important, though, especially limits that involve infinity. | ||
% | ||
%One of the problems addressed by this chapter is this: suppose we know information about a function and its derivatives at a point, such as $f(1) = 3$, $\fp(1) = 1$, $\fp'(1) = -2$, $\fp''(1) = 7$, and so on. What can I say about $f(x)$ itself? Is there any reasonable approximation of the value of $f(2)$? The topic of Taylor Series addresses this problem, and allows us to make excellent approximations of functions when limited knowledge of the function is available. | ||
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%\apexchapter[text/09_Conic_Sections]{Curves in the Plane}{chapter:planar_curves} | ||
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\input{text/07_Shell_Method} | ||
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%\printexercises{exercises/14-03-exercises} | ||
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%\printexercises{standalone/standalone_exercises} | ||
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\appendix | ||
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\printsolutions{Standalone Solutions To All Problems} | ||
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%\printindex | ||
% | ||
%\backmatter | ||
% | ||
%\input{text/Inside_Cover_Of_The_Text_Material_Complete} | ||
\pagestyle{empty} | ||
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\framebox[.14\linewidth][l]{\parbox{1pt}{Chapter\\\chapterautorefname}} | ||
\framebox[.14\linewidth][l]{\parbox{1pt}{Section\\\sectionautorefname}} | ||
\framebox[.14\linewidth][l]{\parbox{1pt}{150.0pt\\\the\marginparwidth}} | ||
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% todo tikz matrix spacing see https://github.com/brucemiller/LaTeXML/issues/794 | ||
\noindent before\\ | ||
\begin{tikzpicture} | ||
\matrix[row sep=3mm,column sep=3mm]{ | ||
\node(left){L}; &&&&&& \node(right){R};\\\\\\\\ | ||
\node(bottom){B};\\ | ||
}; | ||
\draw(left)--(right)(left)--(bottom); | ||
\end{tikzpicture}\quad | ||
\begin{tikzpicture} | ||
\matrix { | ||
& \node (A) {A}; \\ | ||
\node{B};&& \node(C){C}; \\ | ||
}; | ||
\draw (A.south) -- (A|- C.south); | ||
\end{tikzpicture}\\ | ||
after | ||
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Compare: % see 09_Parametric_Equations.tex | ||
\[ | ||
\begin{gathered}\text{Choose}\\t\end{gathered}\quad | ||
\tikz[>=latex,baseline=(current bounding box.center)]{\draw[->](0,.3)--(1,.6);\draw[->](0,-.3)--(1,-.6);}\quad | ||
{\addtolength{\jot}{-.5ex} | ||
\begin{gathered} | ||
\text{Use a function}\\f\text{ to find }x\\\bigl(x=f(t)\bigr)\\~\\ | ||
\text{Use a function}\\g\text{ to find }y\\\bigl(y=g(t)\bigr) | ||
\end{gathered} | ||
}\quad | ||
\tikz[>=latex,baseline=(current bounding box.center)]{\draw[->](0,.6)--(1,.3);\draw[->](0,-.6)--(1,-.3);}\quad | ||
\begin{gathered}\text{Plot point}\\(x,y)\end{gathered} | ||
\] | ||
to: | ||
\[ | ||
\begin{gathered}\text{Choose}\\t\end{gathered}\quad | ||
\begin{gathered} | ||
\rotatebox{-20}{\scalebox{2}{$\nearrow$}}\\ | ||
\rotatebox{20}{\scalebox{2}{$\searrow$}} | ||
\end{gathered}\quad | ||
{\addtolength{\jot}{-.5ex} | ||
\begin{gathered} | ||
\text{Use a function}\\f\text{ to find }x\\\bigl(x=f(t)\bigr)\\~\\ | ||
\text{Use a function}\\g\text{ to find }y\\\bigl(y=g(t)\bigr) | ||
\end{gathered} | ||
}\quad | ||
\begin{gathered} | ||
\rotatebox{20}{\scalebox{2}{$\searrow$}}\\ | ||
\rotatebox{-20}{\scalebox{2}{$\nearrow$}} | ||
\end{gathered}\quad | ||
\begin{gathered}\text{Plot point}\\(x,y)\end{gathered} | ||
\] | ||
to: | ||
\begin{center} | ||
\begin{tikzpicture}[>=latex] | ||
\draw (0,0) node (A) [align=center] {Choose \\$t$} | ||
(3,1) node[align=center] (B1) {Use a function\\ $f$ to find $x$\\$\bigl(x=f(t)\bigr)$} | ||
(3,-1) node[align=center] (B2) {Use a function\\ $g$ to find $y$\\$\bigl(y=g(t)\bigr)$} | ||
(6.25,0) node [align=center] (C) {Plot point \\ $(x,y)$}; | ||
\draw [->](A) --(B1); | ||
\draw [->](A) --(B2); | ||
\draw [->](B1) -- (C); | ||
\draw [->](B2) -- (C); | ||
\end{tikzpicture} | ||
\end{center} | ||
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\begin{sectionexercises} | ||
\item\label{probone} A reference to \ref{probone} should have no decimal after number. | ||
\end{sectionexercises} | ||
in between | ||
\begin{sectionexercises} | ||
\item Should continue numbering. | ||
\end{sectionexercises} | ||
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% see Eg1.3.8 | ||
\[a+b=c\quad\text{because \ref{probone}}\] | ||
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Stuff $\left\{\rule{0pt}{12pt}\right\}$. $\underbrace{\makebox[1.8cm]{}}_a$. | ||
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\begin{tabular}{cc} | ||
here & \multirow{1.5}{*}{should be at the bottom} | ||
% see https://tex.stackexchange.com/a/364935/107497 | ||
\end{tabular} | ||
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\parbox[t]{\linewidth}{\begin{multicols}{2} | ||
\begin{enumerate} | ||
\item\label{thm:d_const_mult_rule} $\frac{d}{d x}\bigl(cf(x) \bigr) = c\cdot f'(x)$ | ||
\item\label{thm:d_sum_diff_rule} $\frac{d}{d x}\bigl(f(x)\pm g(x) \bigr) =$ \\ | ||
\null\qquad$f'(x)\pm g'(x)$ | ||
\item $\frac{d}{d x}\bigl(C \bigr) = 0$ | ||
\setcounter{enumi}{0} | ||
\item $\int c\cdot f(x)d x = c\cdot \int f(x)d x$ | ||
\item $\int \bigl(f(x)\pm g(x)\bigr)d x =$ \\ | ||
\null\qquad$\int f(x)d x\pm \int g(x)d x$ | ||
\item $\int 0d x = C$ | ||
\end{enumerate} | ||
\end{multicols}} | ||
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\end{document} |
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