%Caleb McWhorter
%May 6, 2016

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\fancyhead[R]{\textbf{Math $\mathbf{296}$   \;\;\;\;} \\ \vspace{0.4cm} \textbf{Quiz 8: Polar Coordinates}}
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\begin{document}
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\vspace*{0.1in}

\fbox{\parbox{\textwidth}{\underline{\textbf{Formulae}:} 
 Recall the formula you \emph{\textbf{certainly}} already have memorized for the final:
\[
A=\frac{1}{2} \int_a^b r(\theta)^2 \; d\theta
\]
and this formula
\[
\cos^2\theta=\frac{1+\cos 2\theta}{2}
\]
}} \\ \\

\noindent \ee{1} Find the area of the region inside the circle $r=2\cos \theta$ but outside the circle $r=1$. [You should draw the picture of these circles first.]

\newpage

\pagestyle{empty}
\ee{Bonus} Does the following series diverge or converge? You do not need to justify explicitly why, just give a plausible argument. [Hint: What grows faster - polynomials or logs?]
\[
\sum_{n=25}^\infty \frac{1}{\ln(\ln(\ln(n)))} 
\]

\end{document}