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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 6}\quad {\sl Mar. 7, 1996}

\begin{enumerate}
\problemspace
\item 
  \begin{enumerate}[a)]
  \item Define what the notation $f(x) = o(g(x))$ as $x\to a$ means.

  \answerspace

  \problemspace
  \item Prove that $\frac{1}{1+g(x)} = 1 - g(x) + o(g(x))$, if
  $\lim_{x\to a}g(x) = 0$.

  \answerspace

  \end{enumerate}

\newpage
\item
  \begin{enumerate}[a)]

  \item
  Show that for any constant $c$, $\frac{\log(1 + c x^2 + o(x^2))}{x^2} =
  c + o(1)$.

  \answerspace

  \item 
  Show that $\lim_{x\to0} (\cos(x))^{a/x^2} = 1/\sqrt{e^a}$.

  (Hint: write $\cos(x)^{a/x^2} =\exp[a \log(\cos(x))/x^2]$ and
  use part a) on $\log(\cos(x))$.)

  \answerspace

  \end{enumerate}

\end{enumerate}

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