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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 7}\quad {\sl Nov.\ 3, 1994}

\begin{enumerate}
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\item
    \begin{enumerate}[a)]
    \item State the \textsc{Basic Limit Theorems}. 
    \answerspace

    \item Use the Basic Limit Theorems to prove that if $f$ and $g$ are
    continuous at $p$, then $f + g$ and $f\cdot g$ are continuous at $p$.
    \answerspace

    \end{enumerate}

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\item
  \begin{enumerate}[a)]
  \item State the \textsc{Squeezing Principle}.
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  \item Use the Squeezing Principle to prove $\lim_{t\to0} t \cos(3t^2) = 0$.
  \answerspace

  \end{enumerate}

\problemspace
\item Suppose $f(x)$ is a function with the following property: if $|x - 1| <
3$ then $|f(x) - 5| < 7|x-1|^2$. Given $\epsilon > 0$, determine how $\delta$
should be chosen so that if $|x - 1| < \delta$ then $|f(x) - 5| < \epsilon$.
\answerspace\answerspace

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\item Find $\lim_{x\to1} \frac{\sqrt{x+3} - 2}{x-1}$.
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