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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 8}\quad {\sl Nov.\ 2, 1995}

\begin{enumerate}

\problemspace
\item Prove using the definition of continuity that if $v$ is
continuous at $p$ and $u$ is continuous at $q=v(p)$, then the
composition $u\circ v$ is  continuous at~$p$.
\answerspace

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

  \item State \textsc{Bolzano's Theorem}.
  \answerspace

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

  \end{enumerate}


\newpage
\item Let $f(x) = (x^2-2x)^2+1$ for $x \ge 2$.
  \begin{enumerate}[a)]

  \item Show that $f(x)$ is strictly increasing in its domain $x \ge 2$.
  \answerspace\answerspace

  \item Find a formula for $f^{-1}(x)$ and determine its domain.
  \answerspace\answerspace

  \end{enumerate}

\end{enumerate}

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