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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 7}\quad {\sl Oct.\ 26, 1995}

\begin{enumerate}
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\item
Suppose $\lim_{x\to p} f(x) = A$ and $\lim_{x\to p} g(x) = B$. Prove,
using the definition of the limit, that $\lim_{x\to p} f(x)g(x) = AB$.
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\item
Assume $f(x)$ is integrable on $[a,b]$ and let $F(x) = \int_a^x f(t)\,dt$.
Prove that $F(x)$ is continuous at each point $p\in[a,b]$.
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\item
Calculate the following limits and explain which theorems
you are using.

  \begin{enumerate}[a)]
  \item $\lim_{x\to0} x^2 \cos(\frac{1}{x^2})$.
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  \item $\lim_{x\to1} \frac{(x-1)^2}{\sin^2[3(x^2-1)]}$
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  \item $\lim_{x\to1} \frac{\sqrt{x+3} - 2}{x-1}$.
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  \end{enumerate}

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