\documentclass[12pt]{article}

\usepackage{enumerate}
\usepackage{calculus}
\pagestyle{empty}
\setlength{\parindent}{0pt}
\everymath{\displaystyle}
\newcommand{\answerspace}{\vspace{1.25in}}
\newcommand{\problemspace}{\vfil}

\begin{document}

{\bf Math 165: Honors Calculus I}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

{\bf Quiz 7}\quad {\sl Oct.~29, 1998}

\begin{enumerate}
\item Use the Basic Limit Theorems to prove that if $f$ and $g$ are
    continuous at $p$, then $f + g$ and $f\cdot g$ are continuous at $p$.
    \answerspace


\problemspace
\item Use the Squeezing Principle to show
  $\lim_{x\to0} x^2 \cos\big(\frac{3}{x^2}\big) = 0$.
  \answerspace

\newpage
\item
Compute the following limits. Explain which limit theorems you are using
in each case.

  \begin{enumerate}[a)]
  \item $\lim_{x\to1} \frac{x-1}{\sin[(x^2-1)]}$
  \answerspace

\vfil

  \item $\lim_{x\to0} \frac{\sqrt{x+9} - 3}{x}$
  \answerspace 

\vfil

  \item $\lim_{x\to 3} \sqrt{2 + \cos(\pi x^2)}$
  \answerspace 

\vfil

  \end{enumerate}

\end{enumerate}

\end{document}
