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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/mathexam/doc/sample.tex
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+\documentclass[fleqn]{article}
+\usepackage[left=1in, right=1in, top=1in, bottom=1in]{geometry}
+\usepackage{mathexam}
+\usepackage{amsmath}
+
+\ExamClass{Sample Class}
+\ExamName{Sample Exam}
+\ExamHead{\today}
+
+\let\ds\displaystyle
+
+\begin{document}
+\ExamInstrBox{
+Please show \textbf{all} your work! Answers without supporting work will not be given credit. Write answers in spaces provided. You have 1 hour and 50 minutes to complete this exam.}
+\ExamNameLine
+\begin{enumerate}
+ \item Calculate the following limits. If a limit is $\infty$ or $-\infty$,
+ please say so. Make sure you show all your work and justify all your
+ answers.
+ \begin{enumerate}
+ \item $\ds{\lim_{x\rightarrow3}\frac{\sqrt{x+1} - 2}{x-3}}$\answer
+ \item $\ds{\lim_{x\rightarrow0}\frac{\sin(4x)}{8x}}$\answer
+ \end{enumerate}
+ \item Use the $\varepsilon$-$\delta$ definition of limit to prove that
+ \[\lim_{x\rightarrow 2} x^2 - 3x + 2 = 0\]\noanswer[2.5in]
+ \newpage
+ \item If $h(x) = \sqrt{x^2 + 2} - 1$, find a \textbf{non-trivial} decomposition of $h$ into $f$ and $g$ such that $h = f\circ g$.
+ \answer*{$f(x)=$}\addanswer*{$g(x)=$}
+ \item Find the first two derivatives of the function $f(x) = x^2\cos(x)$. Simplify
+ your answers as much as possible. Show all your work.
+ \answer*{$f'(x)=$}\answer*{$f''(x)=$}
+ \newpage
+ \item Find the derivative of the function $\ds{f(x) = \int_{x^2}^2
+ \frac{\cos(t)}{t} \,dt}$.\answer[1in plus 1fill]
+ \item Set up, but do not evaluate, the integral for the volume of the solid obtained by rotating the area between the curves $y = x$ and $y = \sqrt{x}$ about the $x$-axis.\noanswer
+\end{enumerate}
+\end{document}
+