\documentclass[12pt]{book}

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

\begin{document}

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

{\bf Quiz 8}\quad {\sl Nov.\ 10, 1994}

\begin{enumerate}
\problemspace
\item
  \begin{enumerate}[a)]
    \item Define the composition $u\compose v$ of two functions $u$ and $v$.
    \answerspace

    \item  Let $u(x) = \sqrt{x}$, $v(x) = 4 -  x^2$ and let the
    domain of both functions be $\{x\in \R \, | \, x \ge 0\}$. Determine
    the domain of the composition, $u\compose v$.
    \answerspace

  \end{enumerate}

\problemspace
\item
  \begin{enumerate}[a)]
  \item State \textsc{Bolzano's Theorem}.
  \answerspace

  \item State the \textsc{Intermediate Value Theorem}.
  \answerspace

  \end{enumerate}

\newpage
\item Prove that the equation $\cos(x) = x$ has a solution.

\answerspace\answerspace

\problemspace
\item
  \begin{enumerate}[a)]
  \item Define the inverse of a function $f(x)$.
  \answerspace

  \item Find the inverse of the function $f(x) = x^4 - 2x^2 + 1$, $x \ge 1$.
  \answerspace

  \end{enumerate}


\end{enumerate}

\end{document}
