\documentclass[12pt]{article}

\usepackage{enumerate}
\usepackage{calculus}
\pagestyle{empty}
\setlength{\parindent}{0pt}
%\setlength{\topmargin}{0in}
%\setlength{\headheight}{0in}
%\setlength{\headsep}{0in}
%\setlength{\footskip}{0in}
%\setlength{\textheight}{9in}
\everymath{\displaystyle}
\newcommand{\answerspace}{\vspace{2in}}
\newcommand{\problemspace}{\bigskip}


\begin{document}

{\bf Math 166: Honors Calculus II}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

{\bf Quiz 8}\quad {\sl Mar. 30, 1995}

\begin{enumerate}
\problemspace
\item 
  \begin{enumerate}[a)]
  \item State the Monotone Convergence Theorem for sequences.

  \answerspace

  \problemspace
  \item Prove a) for the case of decreasing sequences.

  \answerspace

   \end{enumerate}


\newpage
\item 
  \begin{enumerate}[a)]

  \item Compute $\lim_{x\to \infty}
  \left(\frac{x-c}{x+c}\right)^x$.

  \answerspace

 
\item Prove $\lim_{n\to \infty} \sum_{k=1}^n \frac{n}{16n^2 - k^2} =
    \frac{1}{8}\log(\frac{5}{3})$. (Hint: the limit equals a certain
    integral.)

  \answerspace

  \end{enumerate}

\end{enumerate}

\end{document}

