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{\bf Math 166: Honors Calculus II}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

{\bf Quiz 5}\quad {\sl Feb. 25, 1999}

\begin{enumerate}
\problemspace
\item

  \begin{enumerate}[a)]

  \item State Taylor's formula with remainder (explain all symbols used).
  \answerspace

  \item Explain the Lagrange form of the remainder in Taylor's Formula.
  \answerspace

  \end{enumerate}

\problemspace
\item 

  \begin{enumerate}[a)]

  \item Prove that $T_{2n+1}(\arctan(x)) = \sum_{k=0}^n
  \frac{(-1)^k}{2k+1}x^{2k+1}$.
  \answerspace

  \item Find a positive integer $n$ such that $T_{2n+1}(\arctan(x))$
  approximates $\arctan(x)$ on the interval $[-1,1]$ with an error no
  greater than $10^{-5}$.  \answerspace

  \end{enumerate}

\end{enumerate}

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