final adjustments to get latexml working

teepeemm · teepeemm · commit f017220008b2 · 2021-11-21T15:06:26.000-06:00
diff --git a/apexNotes.txt b/apexNotes.txt
@@ -1,10 +1,13 @@
 9.6 principle of ratio test: a_n behaves like L^n
+D10.3.2: reword to avoid /0
 
 LaTeXML:
-T5.1.2&3 multicol, numbering
 Some Patrick JMT is forcing viewing on YouTube.  Drop for something else?
-Centering: 2.1, 3.5
 11.1.15ff side by side
+2.4#61, 2.5#49 \\*
+F4.2.3,4: translated right b/c clip&scope?
+F5.3.4 summation notation explanation
+F10.4.7 cmidrule
 
 1.0 figure placement
 3.5 KI 1 break p2 ?
diff --git a/errata/Errata.tex b/errata/Errata.tex
@@ -78,6 +78,7 @@
 \noindent
 The following error exists in the in June 2021 printed version of Apex LT Calculus II:
 \begin{enumerate}
+\item \S7.1\#5 p348: The solution's line segment should go through $(5,-2)$.
 \item \S8.7 p456 Theorem 1: The variable $n$ is representing two different things.  For that matter, so is $M$.
 \label{2021-06-00II}
 \end{enumerate}
diff --git a/exercises/07-07-exercises.tex b/exercises/07-07-exercises.tex
@@ -32,7 +32,7 @@
 \draw[draw={\colorone},thick] (axis cs:-6,1)--(axis cs:-4,4)--(axis cs:-2,5)--(axis cs:0,7);
 \addplot[draw={\colorone},mark=*,only marks] coordinates {(-6,1)(-4,4)(-2,5)(0,7)};
 
-\draw[draw={\colortwo},thick] (axis cs:1,-6)--(axis cs:4,-4)--(axis cs:7,0);
+\draw[draw={\colortwo},thick] (axis cs:1,-6)--(axis cs:4,-4)--(axis cs:5,-2)--(axis cs:7,0);
 \addplot[mark=*,only marks,draw={\colortwo}] coordinates {(1,-6)(4,-4)(5,-2)(7,0)};
 \addplot[domain=-9:9,black, thick,smooth,dashed] {x};
 \node[above] at (axis cs:-4,5) {$f(x)$};
diff --git a/standalone.tex b/standalone.tex
@@ -23,19 +23,11 @@
 
 \mainmatter
 
-\setcounter{chapter}{3}
+\setcounter{chapter}{10}
 
-\setcounter{section}{4}
+\setcounter{section}{3}
 
-%\apexchapter[text/01_Prerequisite]{Limits}{ch:label}
-
-%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.
-
-%\apexchapter[text/09_Conic_Sections]{Curves in the Plane}{chapter:planar_curves}
-
-\input{text/03_Curve_Sketching}
+\input{text/09_Polar_Intro}
 
 %\printexercises{exercises/14-03-exercises}
 
diff --git a/style.css b/style.css
@@ -2,13 +2,13 @@
     display: inline-block;
 }
 
-.twoColumn {
+.columns2,.twoColumn {
     columns: 2
 }
-.threeColumn {
+.columns3,.threeColumn {
     columns: 3
 }
-.fourColumn {
+.columns4,.fourColumn {
     columns: 4
 }
 /*
diff --git a/text/01_Analytic_Limits.tex b/text/01_Analytic_Limits.tex
@@ -116,7 +116,7 @@ \section{Finding Limits Analytically}\label{sec:limit_analytically}
 \begin{theorem}[Limits of Basic Functions]\label{thm:lim_continuous}
 Let $c$ be a real number in the domain of the given function and let $n$ be a positive integer. The following limits hold:
 \begin{multicols}{3}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns3}
 \item	$\ds \lim_{x\to c} \sin x = \sin c$
 \item	$\ds \lim_{x\to c} \cos x = \cos c$
 \item	$\ds \lim_{x\to c} \tan x = \tan c$
@@ -136,7 +136,7 @@ \section{Finding Limits Analytically}\label{sec:limit_analytically}
 \begin{example}[Evaluating limits analytically]\label{ex_limit_1}
 Evaluate the following limits.
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item		$\ds \lim_{x\to \pi} \cos x$
 \item		$\ds \lim_{x\to 3} (\sec^2x - \tan^2 x)$
 \item		$\ds \lim_{x\to \frac\pi2} \cos x\sin x$
@@ -286,7 +286,7 @@ \section{Finding Limits Analytically}\label{sec:limit_analytically}
 \begin{theorem}[Special Limits]\label{thm:special_limits}
 \mbox{}\vspace{-1.5\baselineskip}
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 	\item		$\ds \lim_{x\to 0} \frac{\sin x}{x} = 1$
 	\item		$\ds \lim_{x\to 0} \frac{\cos x-1}{x} = 0$
 	\item		$\ds \lim_{x\to 0} (1+x)^\frac1x = e$
diff --git a/text/01_Continuity.tex b/text/01_Continuity.tex
@@ -171,7 +171,7 @@ \section{Continuity}\label{sec:continuity}
 \begin{example}[Determining intervals on which a function is continuous]\label{ex_cont_funct1}
 For each of the following functions, give the domain of the function and the interval(s) on which it is continuous.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$f(x) = 1/x$
 		\item	$f(x) = \sin x$
 		\item	$f(x) = \sqrt{x}$
@@ -230,7 +230,7 @@ \section{Continuity}\label{sec:continuity}
 \begin{theorem}[Continuous Functions]\label{thm:continuous_functions}
 The following functions are continuous on their domains.\index{continuous function!properties}
 \begin{multicols}{2}
- \begin{enumerate}
+ \begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds f(x) = \sin x$
 		\item	$\ds f(x) = \cos x$
 		\item	$\ds f(x) = \tan x$
@@ -258,7 +258,7 @@ \section{Continuity}\label{sec:continuity}
 \begin{example}[Determining intervals on which a function is continuous]\label{ex_cont_funct}
 State the interval(s) on which each of the following functions is continuous.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds f(x) = \sqrt{x-1} + \sqrt{5-x}$
 		\item	$\ds f(x) = x\sin x$
 		\item	$\ds f(x) = \tan x$
diff --git a/text/01_Limits_Involving_Infinity.tex b/text/01_Limits_Involving_Infinity.tex
@@ -364,7 +364,7 @@ \subsection{Limits at Infinity and Horizontal Asymptotes}
 \begin{example}[Finding limits of rational functions]\label{ex_hzasy3}
 (a) Analytically evaluate the following limits, and (b) Use \autoref{thm:lim_rational_fn_at_infty} to evaluate each limit.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds\lim_{x\to-\infty}\frac{x^2+2x-1}{x^3+1}$
 		\item	$\ds\lim_{x\to\infty}\frac{x^2+2x-1}{1-x-3x^2}$
 		\item	$\ds\lim_{x\to\infty}\frac{x^2-1}{3-x}$
diff --git a/text/01_One_Sided_Limits.tex b/text/01_One_Sided_Limits.tex
@@ -57,7 +57,7 @@ \section{One Sided Limits}\label{sec:limit_continuity}
 \end{tikzpicture}}% ends the mtable
 %
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item	$\ds \lim_{x\to 1^-} f(x)$
 \item	$\ds \lim_{x\to 1^+} f(x)$
 \item	$\ds \lim_{x\to 1} f(x)$
@@ -98,7 +98,7 @@ \section{One Sided Limits}\label{sec:limit_continuity}
 \begin{example}[Evaluating limits of a piecewise-defined function]\label{ex_onesideb}
 Let $f(x) = \begin{cases} 2-x & 0<x<1 \\ (x-2)^2 & 1<x<2 \end{cases},$ as shown in \autoref{fig:onesidedb}. Evaluate the following.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds \lim_{x\to 1^-} f(x)$
 		\item	$\ds \lim_{x\to 1^+} f(x)$
 		\item	$\ds \lim_{x\to 1} f(x)$
@@ -157,7 +157,7 @@ \section{One Sided Limits}\label{sec:limit_continuity}
 \end{tikzpicture}}
 %
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds \lim_{x\to 1^-} f(x)$
 		\item	$\ds \lim_{x\to 1^+} f(x)$
 		\item	$\ds \lim_{x\to 1} f(x)$
@@ -171,7 +171,7 @@ \section{One Sided Limits}\label{sec:limit_continuity}
 \begin{example}[Evaluating limits of a piecewise-defined function]\label{ex_onesided}
 Let $f(x) = \begin{cases} x^2 & 0\leq x\leq 1 \\ 2-x & 1<x\leq 2\end{cases}.$ Evaluate the following.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds \lim_{x\to 1^-} f(x)$
 		\item	$\ds \lim_{x\to 1^+} f(x)$
 		\item	$\ds \lim_{x\to 1} f(x)$
@@ -191,7 +191,7 @@ \section{One Sided Limits}\label{sec:limit_continuity}
 \begin{example}[Evaluating limits of an absolute value function]\label{ex_absvalue}
 Let $f(x) =\dfrac{\abs{x-1}}{x-1}.$ Evaluate the following.
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds \lim_{x\to 1^-} f(x)$
 		\item	$\ds \lim_{x\to 1^+} f(x)$
 		\item	$\ds \lim_{x\to 1} f(x)$
diff --git a/text/01_Prerequisite.tex b/text/01_Prerequisite.tex
@@ -6,7 +6,7 @@ \subsection{Functions}
 
 A \textbf{function} $f$ is a rule that assigns each element $x$ from a set (called the domain) to exactly one element, called $f(x)$, in another set. Unless we say otherwise, the \textbf{domain} is the set of all real numbers for which the rule makes sense and defines a real number. All possible values of $f(x)$ are called the \textbf{range} of $f$. We use four ways to represent a function.
 \begin{multicols}{2}
-\begin{itemize}
+\begin{itemize}\lxAddClass{columns2}
 \item By a graph
 \item By an explicit formula
 \item By a table of values
@@ -139,8 +139,8 @@ \subsection{Functions}
 
 %\begin{example}[Sketching with basic transformations]\label{ex_prereq_sketch}
 %Sketch the graph of the following functions using the base function and the appropriate transformations.
-%\begin{enumerate}
 %\begin{multicols}{2}
+%\begin{enumerate}\lxAddClass{columns2}
 %\item $y=\displaystyle \frac{1}{x+3}$
 %\item $y=\sqrt{x+3}+1$
 %\item $y=\abs{x-4}$
diff --git a/text/02_Chain_Rule.tex b/text/02_Chain_Rule.tex
@@ -161,7 +161,7 @@ \section{The Chain Rule}\label{sec:chainrule}
 The following is a short list of how the Chain Rule can be quickly applied to familiar functions.
 
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 	\item	$\ds\frac{\dd}{\dd x}\Bigl(u^n\Bigr) = n\cdot u^{n-1}\cdot u\primeskip'.$
 	\item	$\ds\frac{\dd}{\dd x}\Bigl(e^u\Bigr) = u\primeskip'\cdot e^u.$
 	\item	$\ds\frac{\dd}{\dd x}\Bigl(\sin u\Bigr) = u\primeskip'\cdot \cos u.$
diff --git a/text/02_Derivative.tex b/text/02_Derivative.tex
@@ -144,7 +144,7 @@ \section{Instantaneous Rates of Change: The Derivative}\label{sec:derivative}
 \begin{example}[Finding derivatives and tangent lines]\label{ex_derv_point1}
 Let $f(x) = 3x^2+5x-7$. Find: 
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 	\item		$\fp(1)$
 	\item		The equation of the tangent line to the graph of $f$ at $x=1$.
 	\item		$\fp(3)$
diff --git a/text/02_Derivative_Inverse_Functions.tex b/text/02_Derivative_Inverse_Functions.tex
@@ -148,7 +148,7 @@ \section{Derivatives of Inverse Functions}\label{sec:deriv_inverse_function}
 \begin{theorem}[Derivatives of Inverse Trigonometric Functions]\label{thm:deriv_inverse_trig}
 The inverse trigonometric functions are differentiable on all open sets contained in their domains (as listed in \autoref{fig:domain_trig}) and their derivatives are as follows:\index{derivative!inverse trig.}
 \begin{multicols}{2}
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 		\item	$\ds\frac \dd{\dd x}\bigl(\sin^{-1}x\bigr)= \frac1{\sqrt{1-x^2}}$ 
 		\item	$\ds\frac \dd{\dd x}\bigl(\sec^{-1}x\bigr)= \frac1{\abs{x}\sqrt{x^2-1}}$
 		\item	$\ds\frac \dd{\dd x}\bigl(\tan^{-1}x\bigr)= \frac1{1+x^2}$
diff --git a/text/04_Optimization.tex b/text/04_Optimization.tex
@@ -149,10 +149,14 @@ \section{Optimization}\label{sec:optimization}
 %\mnote{\textbf{Note:} \autoref{ex_opt3} is another classic calculus example. The underlying principle is given in a variety of contexts; Google ``calculus dog'' to find articles where }
 
 \mtable{Running a power line from the power station to an offshore facility with minimal cost in \autoref{ex_opt3}.}{fig:opt3b}{\begin{tikzpicture}[>=latex]
-\begin{scope}
-\clip (0,0) rectangle (120pt,50pt);
-\draw [inner color={\colorone},draw = white] (-10,-25pt) rectangle (160pt,70pt);
-\end{scope}
+\ifbool{latexml}{
+ \draw[inner color={\colorone},draw=white](0,0)rectangle(120pt,50pt);
+}{%
+ \begin{scope}
+  \clip (0,0) rectangle (120pt,50pt);
+  \draw [inner color={\colorone},draw = white] (-10,-25pt) rectangle (160pt,70pt);
+ \end{scope}
+}
 \draw [top color=brown, bottom color=white,draw=white] (0,0) rectangle (120pt,-15pt);
 \draw (0,0) -- (140pt,0);
 \filldraw [fill=white] (10pt,-5pt) rectangle (20pt,5pt);
@@ -176,10 +180,14 @@ \section{Optimization}\label{sec:optimization}
 The optimal solution likely has the line being run along the ground for a while, then underwater, as the figure implies. We need to label our unknown distances --- the distance run along the ground and the distance run underwater. Recognizing that the underwater distance can be measured as the hypotenuse of a right triangle, we choose to label the distances as shown in \autoref{fig:opt3c}.
 
 \mtable{Labeling unknown distances in \autoref{ex_opt3}.}{fig:opt3c}{\begin{tikzpicture}[>=latex]
-\begin{scope}
-\clip (0,0) rectangle (120pt,50pt);
-\draw [inner color={\colorone},draw = white] (-10,-25pt) rectangle (160pt,70pt);
-\end{scope}
+\ifbool{latexml}{
+ \draw[inner color={\colorone},draw=white](0,0)rectangle(120pt,50pt);
+}{%
+ \begin{scope}
+  \clip (0,0) rectangle (120pt,50pt);
+  \draw [inner color={\colorone},draw = white] (-10,-25pt) rectangle (160pt,70pt);
+ \end{scope}
+}
 \draw [top color=brown, bottom color=white,draw=white] (0,0) rectangle (120pt,-15pt);
 \draw (0,0) -- (130pt,0);
 \filldraw [fill=white] (10pt,-5pt) rectangle (20pt,5pt);
diff --git a/text/05_Antiderivatives.tex b/text/05_Antiderivatives.tex
@@ -127,7 +127,7 @@ \section{Antiderivatives and Indefinite Integration}\label{sec:antider}
 \begin{theorem}[Derivatives and Antiderivatives]\label{thm:indef_alg}
 \mbox{}\\[-2.5\baselineskip]
 \parbox[t]{\linewidth}{\begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item\label{thm:d_const_mult_rule} $\frac{\dd}{\dd x}\bigl(cf(x) \bigr) = c\cdot \fp(x)$
 \item\label{thm:d_sum_diff_rule} $\frac{\dd}{\dd x}\bigl(f(x)\pm g(x) \bigr) =$ \\
 \null\qquad$\fp(x)\pm g'(x)$
@@ -161,7 +161,7 @@ \section{Antiderivatives and Indefinite Integration}\label{sec:antider}
 \tcbset{grow to right by=2em}
 \begin{theorem}[Derivatives and Antiderivatives]\label{thm:common_indef_alg}
 \mbox{}\\[-2.5\baselineskip]
-\parbox[t]{\linewidth}{\begin{multicols}{2}
+\parbox[t]{\linewidth}{\begin{multicols}{2}\lxAddClass{columns2}
 Common Derivatives
 \begin{enumerate}\setcounter{enumi}{3}
 \item\label{thm:d_power_rule} $\frac{\dd}{\dd x}\bigl(x^n \bigr) = n\cdot x^{n-1}
diff --git a/text/05_Definite_Integral.tex b/text/05_Definite_Integral.tex
@@ -138,7 +138,7 @@ \section{The Definite Integral}\label{sec:def_int}
 \end{tikzpicture}}
 %
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 	\item	$\ds \int_0^3 f(x)\dd x$
 	\item	$\ds \int_3^5 f(x)\dd x$
 	\item	$\ds \int_0^5 f(x)\dd x$
diff --git a/text/05_Riemann_Sums.tex b/text/05_Riemann_Sums.tex
@@ -225,7 +225,7 @@ \subsection{Summation Notation}
 \begin{tikzpicture}[>=latex]
 \draw  (1,1) node {$\displaystyle \sum_{i=1}^9 a_i$.};
 \draw [draw={\colorone}] (-.2,0) node [text width=45pt,align=center](a)
- {\scriptsize \centering $i$=index \\[-5pt] of summation};
+ {\scriptsize \centering $i$=index \\[-5pt] of~summation};
 \draw [draw={\colorone},->] (a) -- (.6,.5);
 \draw [draw={\colorone}] (2,0) node [text width=20pt,align=center] (b)
  {\scriptsize \centering lower\\[-5pt] bound};
@@ -236,7 +236,7 @@ \subsection{Summation Notation}
 \draw [draw={\colorone}] (2,2) node [text width=32pt,align=center] (d)
  {\scriptsize \centering summand};
 \draw [draw={\colorone},->] (d) -- (1.4,1.2);
-\draw [draw={\colorone}] (-1,1) node [text width=50pt,align=center] (e) {\scriptsize \centering summation \\[-1pt] symbol \\[-1pt] (an upper case\\[-5pt] sigma)};
+\draw [draw={\colorone}] (-1,1) node [text width=50pt,align=center] (e) {\scriptsize \centering summation \\[-1pt] symbol \\[-1pt] (an~upper~case\\[-5pt] sigma)};
 \draw [draw={\colorone},->] (e) -- (.6,1);
 \end{tikzpicture}
 \caption{Understanding summation notation.}\label{fig:rie_notation}
@@ -279,7 +279,7 @@ \subsection{Summation Notation}
 \mbox{}\\[-\baselineskip]\parbox[t]{\linewidth}{%
 \begin{multicols}{2}
 \index{summation!properties}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 	\item	$\ds \sum_{i=1}^n c = c\cdot n$, where $c$ is a constant.
 	\item	$\ds \sum_{i=m}^n (a_i\pm b_i) = \sum_{i=m}^n a_i \pm \sum_{i=m}^n b_i$
 	\item	$\ds \sum_{i=m}^n c\cdot a_i = c\cdot\sum_{i=m}^n a_i$
diff --git a/text/06_Hyperbolic_Functions.tex b/text/06_Hyperbolic_Functions.tex
@@ -45,7 +45,7 @@ \section{Hyperbolic Functions}\label{sec:hyperbolic}
 \begin{definition}[Hyperbolic Functions]\label{def:hyperbolic_functions}
 \mbox{}\\[-2\baselineskip]\parbox[t]{\linewidth}{%
 \begin{multicols}{2}\index{hyperbolic function!definition}%
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item		$\ds \cosh x = \frac{e^x+e^{-x}}2$
 \item		$\ds \sinh x = \frac{e^x-e^{-x}}2$
 \item		$\ds \tanh x = \frac{\sinh x}{\cosh x}$
@@ -140,7 +140,7 @@ \section{Hyperbolic Functions}\label{sec:hyperbolic}
 \begin{example}[Exploring properties of hyperbolic functions]\label{ex_hf1}
 Use \autoref{def:hyperbolic_functions} to rewrite the following expressions.
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item		$\cosh^2 x-\sinh^2x$
 \item		$\tanh^2 x+\sech^2 x$
 \item		$2\cosh x\sinh x$
@@ -207,7 +207,7 @@ \section{Hyperbolic Functions}\label{sec:hyperbolic}
 {
 \tcbset{grow to right by=16em}
 \begin{keyidea}[Useful Hyperbolic Function Properties]\label{idea:hyperbolic_identities}
-\lxAddClass{threeColumns}
+\lxAddClass{columns3}
 \begin{minipage}[t]{.33\linewidth}
 \textbf{Basic Identities}\par
 \index{hyperbolic function!identities}\index{hyperbolic function!derivatives}\index{hyperbolic function!integrals}\index{derivative!hyperbolic funct.}\index{integration!hyperbolic funct.}%
@@ -404,7 +404,7 @@ \subsection{Inverse Hyperbolic Functions}
 \mbox{}\\[-2\baselineskip]%
 \index{hyperbolic function!inverse!logarithmic def.}%
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item $\ds\cosh^{-1}x=\ln\bigl(x+\sqrt{x^2-1}\bigr)$;\\\null\qquad $x\geq1$
 \item $\ds\tanh^{-1}x=\frac12\ln\left(\frac{1+x}{1-x}\right)$;\\\null\qquad$\abs x<1$
 \item $\ds\sech^{-1}x=\ln\left(\frac{1+\sqrt{1-x^2}}x\right)$;\\\null\qquad$0<x\leq1$
@@ -438,7 +438,7 @@ \subsection{Inverse Hyperbolic Functions}
 \index{hyperbolic function!inverse!derivative}\index{derivative!inverse hyper.}
 \mbox{}\\[-2\baselineskip]\parbox[t]{\linewidth}{%
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item $\ds\frac\dd{\dd x}\bigl(\cosh^{-1}x\bigr)=\frac1{\sqrt{x^2-1}}$;\\\null\qquad$x>1$
 \item $\ds\frac\dd{\dd x}\bigl(\sinh^{-1}x\bigr)=\frac1{\sqrt{x^2+1}}$\\\vphantom{$x\ne0$}
 \item $\ds\frac\dd{\dd x}\bigl(\tanh^{-1}x\bigr)=\frac1{1-x^2}$;\\\null\qquad$\abs x<1$
@@ -479,7 +479,7 @@ \subsection{Inverse Hyperbolic Functions}
 \begin{example}[Derivatives and integrals involving inverse hyperbolic functions]\label{ex_hf3}
 Evaluate the following.
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item	$\ds \frac{\dd}{\dd x}\left[\cosh^{-1}\left(\frac{3x-2}{5}\right)\right]$
 \item	$\ds \int\frac{1}{x^2-1}\dd x$
 \item	$\ds \int \frac{1}{\sqrt{9x^2+10}}\dd x$
diff --git a/text/06_Substitution.tex b/text/06_Substitution.tex
@@ -206,7 +206,7 @@ \subsection{Integrals Involving Trigonometric Functions}
 \mbox{}\\[-2\baselineskip]\parbox[t]{\linewidth}{%
 \addtolength{\columnsep}{-4.5em}% 5 sufficient ; 4 insufficient
 \begin{multicols}{2}\index{integration!of trig. functions}\small
-	\begin{enumerate}
+	\begin{enumerate}\lxAddClass{columns2}
 	\item	$\ds \int \sin x \dd x = -\cos x +C$
 	\item	$\ds\int \cos x\dd x = \phantom{-}\sin x + C$
 	\item	$\ds \int \tan x\dd x = \ln\abs{\sec x}+C$
diff --git a/text/07_Exp_Log_Functions.tex b/text/07_Exp_Log_Functions.tex
@@ -36,7 +36,7 @@ \subsection{General exponential functions}
 \begin{keyidea}[Properties of Exponential Functions]\label{ki_exp_func_props}
 For $a>0$ and $a\neq1$ the exponential function $f(x)=a^x$ satisfies:
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
  \item $a^0=1$
  \item $\ds\lim_{x\to\infty}a^x=\begin{cases}\infty&a>1\\0&a<1\end{cases}$
  \item $a^x>0$ for all $x$
@@ -190,7 +190,7 @@ \subsection{Antiderivatives}
 \begin{theorem}[Derivatives and Antiderivatives of Exponentials and Logarithms]\label{thm_int_exp_log}
 Given a base $a>0$ and $a\neq 1$, the following hold:\\[-1.5\baselineskip]
 \begin{multicols}{2}
-\begin{enumerate}
+\begin{enumerate}\lxAddClass{columns2}
 \item $\dfrac\dd{\dd x}e^x=e^x$
 \item $\dfrac\dd{\dd x}a^x=a^x\ln a$
 \item $\dfrac\dd{\dd x}\ln x=\dfrac1x$
diff --git a/text/08_Integral_Test.tex b/text/08_Integral_Test.tex
diff --git a/text/08_Sequences.tex b/text/08_Sequences.tex
diff --git a/text/09_Polar_Intro.tex b/text/09_Polar_Intro.tex
diff --git a/text/Inside_Cover_Of_The_Text_Material_Complete.tex b/text/Inside_Cover_Of_The_Text_Material_Complete.tex

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