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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 2}\quad {\sl Feb. 2, 1995}

\begin{enumerate}
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\item 
  \begin{enumerate}[a)]
  \item Define the natural logarithm function, $\log(x)$.
  \answerspace
  \item Prove that $\log(ab) = \log(a) + \log(b)$ for $a,b>0$.
  \answerspace
  \item Define the natural exponential function, $\exp(x)$.
  \answerspace
  \item Define $a^x$ for $a>0$ and $x\in\R$.
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\item  Compute the following integrals. (Justify your answers.)
  \begin{enumerate}[a)]
  \item 
  $\int \tan(x)\,dx$
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  \item 
  $\int x \log^2(x)\,dx$
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  \item 
  $\int x 2^{-3x^2}\,dx$
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  \end{enumerate}

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