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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 6}\quad {\sl March 9, 2000}

\begin{enumerate}

\item

  \begin{enumerate}[a)]

  \item Define the symbol $o(g(x))$ as $x\to a$.

  \answerspace

  \item Show that $f(x)o(g(x)) = o(f(x)g(x))$ as $x\to a$.

  \answerspace

  \end{enumerate}

\problemspace

\item
Find a cubic polynomial $p(x)$ such that $\frac{1}{x} = p(x) +
o\big((x-1)^3\big)$ as $x\to1$.

\answerspace

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\item
Use Taylor polynomials and $o$-symbols to compute the limit
\[ \lim_{x\to0}\frac{1}{x^2}\Big(\frac{1}{\cos(x)} - 1\Big) \]

\answerspace

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