\documentstyle[12pt]{report} \setlength{\oddsidemargin}{0.0in} \setlength{\textwidth}{6.5in} \setlength{\topmargin}{0.0in} \setlength{\headheight}{0.0in} \setlength{\headsep}{0.0in} \setlength{\textheight}{9in} \begin{document} \noindent {\large\bf Information for Test 2} \bigskip \noindent {\bf Office Hrs:} Usual (T: 6-7), Extra (T: 4-5, R: 1:30-2:30). \noindent {\bf Calculator:} OK. \noindent {\bf 3$\times$5 Card:} OK. \bigskip \noindent {\bf Advice:} Look over old quizzes and HW problems. If you missed points on a problem, know why you missed them! \bigskip \noindent {\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} \bigskip \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} \bigskip \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} \bigskip \noindent {\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} \end{document}