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\noindent {\LARGE M}{\large ath} {\LARGE 120} {\LARGE S}{\large pring} {\LARGE 98}
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{\Large Quiz {\bf 6}}\hspace{7cm} & \hspace{1.65in} & Basic~Calculus~2\\
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Name: \makebox[2in]{\hrulefill}  & \hspace{1.5in} & \\
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Date: \makebox[2in]{\hrulefill} & \hspace{1.5in} & {\bf Friday March 27, 1998} \\
Time Begun: \makebox[2in]{\hrulefill} & \hspace{1.5in} & Ron Buckmire \\ 
Time Ended: \makebox[2in]{\hrulefill} & \hspace{1.5in} &  \\
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{\Large {\bf Topic covered:}} Improper Integrals

{\small The idea behind this quiz is to give you more practice evaluating improper integrals and to review the inverse trigonometric function $\arctan (x)$.}

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{\Large {\bf Instructions: }}
\begin{itemize}
\item[1.] Once you open the quiz, you have 60 minutes to complete it.
\item[2.] You may use the book or any of your class notes, and you may use a calculator.  You must work alone.
\item[3.] If you use your own paper, please staple it to the quiz before coming to class.  If you don't have a stapler, buy one.
\item[4.] After completing the quiz, sign the pledge below stating on your honor that you have adhered to these rules.  
\item[5.] Relax and enjoy...
\item[6.] {\bf This quiz is due on Monday, March 30}, in class.  NO LATE QUIZZES WILL BE ACCEPTED.
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{\bf Pledge:} I, \makebox[2in]{\hrulefill}, pledge my honor as a human being and Occidental student, that I have followed all the rules above to the letter and in spirit.
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Math 120 Spring 1998 \hfill{Quiz {\bf 6}}
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\vspace{-7.5ex}   {\large\bf SHOW ALL YOUR WORK}\\
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\begin{itemize}
\item[1.] ({\it 2 points}) Compute the derivative of $f(x) = \arctan(2 x)$. (The inverse of the trigonometric function $\tan (x)$ is known as $\arctan(x)$.)
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\item[2.] ({\it 4 points}) Your answer above should assist you in finding the antiderivative of ${\displaystyle \frac{4}{1+(2x)^2}}$. That is, evaluate the following integral.\\
${\displaystyle \int \frac{4}{1+4x^2} \, dx} = $
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\item[3.] ({\it 4 points}) Use your answer from (2) to determine whether the following improper integral converges to a finite value or not. If it converges, compute its value {\it exactly}.\\
${\displaystyle \int_0^{\infty} \frac{4}{1+4x^2} \, dx} = $
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