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{\bf Math 165: Honors Calculus I}

{\bf Assignment 23}\quad {\sl Nov. 13, 1998}

\bigskip
\begin{enumerate}
\item Use the definition of the derivative to find the derivative of the
following functions at any point in their domains.

  \begin{enumerate}[a)]
  \item $f(x) = \frac{1}{x^n}$

  \item $f(x) = \sqrt{x+1}$

  \item $f(x) = \frac{x-1}{x+1}$

  \end{enumerate}

\bigskip
\item Let
\[
f(x) = \left\{\begin{array}{ll}
\frac{\sin(5x^2)}{x} & \mbox{if $x\ne 0$}\\
0                    & \mbox{if $x = 0$}
\end{array}\right.
\]
Use the definition of the derivative to show $f'(0) = 5$.

\end{enumerate}

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