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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 2}\quad {\sl Jan. 28, 1999}

\begin{enumerate}
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\item 
  \begin{enumerate}[a)]
  \item Define the natural logarithm function, $\log(x)$,
  and the natural exponential function, $\exp(x)$.
  \answerspace
  \item Define $a^x$ for $a>0$ and $x\in\R$.
  \answerspace
  \item Prove that $\log(xy) = \log(x)+\log(y)$, $x, y>0$.
  \answerspace
  \end{enumerate}

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\item  Compute the following integrals. (Justify your answers.)
  \begin{enumerate}[a)]
  \item 
  $\int \sec(x)\,dx$
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  \item 
  $\int x \log(x)\,dx$
  \answerspace
  \item 
  $\int_0^1 2^{-x}\,dx$
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  \end{enumerate}

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