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\centerline{MATH 134 -- Calculus with Fundamentals 2}
\centerline{Makeup Quiz 8 -- April 30, 2018}
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\noindent
Your Name: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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\noindent
{\it Directions}
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There are 30 total points possible (distributed as indicated in the questions on both sides).  
You may use a calculator, but not a phone or
any other electronic device.  
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\noindent
\begin{enumerate}
\item[(A)] (10) Find the general solution of the differential equation 
$$\frac{dy}{dx} = \sec(y)\left(x^2 + \frac{1}{x^2}\right)$$
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\item[(B)] (5)  Your answer from part (A) should contain an arbitrary constant.  For which
value of that constant does the solution satisfy the initial condition $y(1) = 0$?  
\end{enumerate}
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\begin{enumerate}
\item[(C)]  (15) How much money do you need to deposit today in an account bearing
$5\%$ interest per year, compounded continuously, in order to have a total of $\$200000$
after $20$ years?
\end{enumerate}
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\caption{The region for Problems A and C.}
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\begin{enumerate}
\item[(C)]  (10) Refer again to the region shown in Figure 1.  Set up 
the integral for the \emph{volume} of the solid generated by rotating that 
region about the line $y =-1$.  \emph{You are not to compute the integral, just 
set it up.}
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\end{enumerate}


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