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\begin{document}

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

{\bf Quiz 5}\quad {\sl Feb. 22, 1996}

\begin{enumerate}
\problemspace
\item
  Use an appropriate substitution to transform the integral 
  $$\int \frac{1}{\cos^2(\theta) + \sin(\theta) + 1}\,d\theta$$
  into an integral of a rational function. (Do not evaluate the integral.)
  \answerspace

\problemspace
\item 
  \begin{enumerate}[a)]
  \item Define the Taylor polynomial $T_n(f;a)$
  \answerspace

  \problemspace
  \item State the following properties of $T_n(f)$: the Linearity
  Property, the Differentiation Property, the Integration Property, and
  the Substitution Property.
  \answerspace

  \item 
  Calculate $T_{3n}\left(\frac{1}{8 + x^3}\right)$.
  \answerspace

  \end{enumerate}

\end{enumerate}

\end{document}
