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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 7}\quad {\sl March 23, 2000}

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\item Define precisely $\lim_{x\to \infty}f(x) = L$.

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\item
Prove that if $\lim_{x\to a}\frac{f(x)}{g(x)} = \infty$ then
$\lim_{x\to a}\frac{g(x)}{f(x)} = 0$.

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\item Compute the limits:

  \begin{enumerate}[a)]

  \item $\lim_{x\to 0}\frac{x \cos(x) - \sin(x)}{x^3}$

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  \item $\lim_{x\to \infty} x^4 \big(e^{1/x^2}-1) - x^2$

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  \item  $\lim_{x\to \infty}\Big(\frac{x+1}{x-1}\Big)^x$

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