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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 3}\quad {\sl Feb. 4, 1999}

\begin{enumerate}
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\item Compute the derivative of $f(x) = \Bigl[\sqrt{2+\sin(x)}\Bigr]^{1+x^3}$.
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\item 
  \begin{enumerate}[a)]
  \item Define $\sinh(x)$, and derive a formula for $\sinh^{-1}(x)$.
  \answerspace
  \item Integrate $\int \frac{1}{\sqrt{x^2 + 2x + 2}}\,dx$.
  \answerspace

  \end{enumerate}

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\item 
  \begin{enumerate}[a)]
  \item State the Theorem on Derivatives of Inverse Functions.
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  \item Let $f(x) = x^5 + 2x^3 + 3x$. Compute $(f^{-1})'(x)$ for $x = 0$
  and $x = 6$.
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  \end{enumerate}

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