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{\large\bf Information for Test 2}

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{\bf Office Hrs:} Usual (T: 6-7), Extra (T: 4-5, R: 1:30-2:30).

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{\bf Calculator:} OK. 

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{\bf 3$\times$5 Card:} OK. 

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{\bf Advice:} Look over old quizzes and HW problems.
If you missed points on a problem, know why you missed them!

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{\bf Test Covers:} 
\begin{itemize}
\item 7.2--7.8 excluding 7.6 (Fluid Pressure).
\item 8.1--8.6
\item 9.1--9.2
\end{itemize}

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\noindent
{\bf Details:}
\begin{itemize}
\item Chapter 7: Volumes of solids of revolution: disk, washer,
shell methods. Arc length and surface area. Work. Centroid/center
of mass.
\item Chapter 8: Integration by parts. Partial fractions
expansion of rational functions. Trigonometric substitution.
Use of tables. Improper integrals, including comparison test
and limit comparison test.
\item Chapter 9: Sequences and series, including theorems
for establishing convergence.
\end{itemize}

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\noindent
{\bf Fine Details:}
\begin{itemize}
\item Chapter 7: (40+ \%) Expect to set up and evaluate
one or two integrals involving volume, arc length, surface area
OR centroid/center of mass.
\item Chapter 8: (40+ \%) Expect to integrate by parts.
Expect to calculate the partial fractions expansion
of a rational function. Expect to use trigonometric substitution.
Expect an improper integral.
\item Chapter 9: (20- \%) Know the difference between a
sequence and a series. Know definitions for convergence of 
sequences and series, and know how to establish
convergence/divergence in the cases we considered.
\end{itemize}

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{\bf Practice:}
\begin{itemize}
\item Find the volume of the ``squashed doughnut'' 
generated by rotating the interior of the ellipse
$4x^2 + (y-3)^2 = 4$ around the $x$-axis.
\item Evaluate $\int_0^{\pi/6}
\frac{2\sin(x)\cos(x)\;dx}{3-3\sin(x)-\cos^2(x)}$.
\item Does $\int_0^{\infty} e^{-x}\sin(x)\;dx$ converge? If so,
evaluate it.
\item Which real number has the base 2 expansion $.011\overline{011}$?
\end{itemize}

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