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%\header{MATH 11}{Exam 1}{Fall 2016}
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\begin{center}\huge MATH 3315 - EXAM 1 - FALL 2017\\
\vspace*{2in}
\large Name: \makebox[3in]{\hrulefill}\\
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\begin{flushleft}\vspace{0.5in}
Friday 8 September 2017\\
Instructor: Tom Cuchta
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\textbf{Instructions:}
\begin{itemize}
	\item  Show all work, clearly and in order, if you want to get full
	credit. If you claim something is true \textbf{you must show work backing up your claim}. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct).
	\item Justify your answers algebraically whenever possible to ensure full credit. 	
	\item  Circle or otherwise indicate your final answers.
	\item  Please keep your written answers brief; be clear and to the point.
	\item  Good luck!
\end{itemize}
\vspace*{10pt}
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\begin{questions} 
\question[36] Compute the following derivatives. 
\begin{parts}
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}x} \log(5x^2+3x+1)$. 
\vfill
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}x} (e^{5x}+e^{7x}+1)^3$
\vfill
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}t} \arcsin(7x^3-9)$
\vfill
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}z} 3^{5z-1}$
\vfill
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}t} \dfrac{\cosh(t)}{\sinh(t)+1}$
\vfill
\part[6] $\dfrac{\mathrm{d}}{\mathrm{d}w} \log(\log(\log(w)))$
\vfill
\end{parts}
\newpage
\question[36] Compute the following indefinite integrals.
\begin{parts}
\part[6] $\displaystyle\int \dfrac{1}{2+x^2} \mathrm{d}x$
\vfill
\part[6] $\displaystyle\int \dfrac{w-5}{w^2+1} \mathrm{d}w$
\vfill
\part[6] $\displaystyle\int \dfrac{4v+4}{2v^2+4v+18} \mathrm{d}v$
\vfill
\part[6] $\displaystyle\int \mathrm{coth}(\theta) \mathrm{d}\theta$ $\Bigg($recall: $\mathrm{coth}=\dfrac{\cosh}{\sinh}$ $\Bigg)$
\vfill
\part[6] $\displaystyle\int \dfrac{\cosh(t)}{\sinh(t)+1} \mathrm{d}t$
\vfill
\part[6] $\displaystyle\int \dfrac{17}{\sqrt{1-2w^2}} \mathrm{d}w$
\vfill
\end{parts}
\newpage
\question[28] Compute the following definite integrals.
\begin{parts}
\part[7] $\displaystyle\int_0^1 7^x - 11^x \mathrm{d}x$
\vfill
\part[7] $\displaystyle\int_2^3 \dfrac{1}{\sqrt{16y^2+1}} \mathrm{d}y$
\vfill
\part[7] $\displaystyle\int_0^3 \xi^4+3\xi^2+\xi+1 \mathrm{d}\xi$
\vfill
\part[7] $\displaystyle\int_1^2 \dfrac{1}{57-4z^2} \mathrm{d}z$
\vfill
\end{parts}


\end{questions}
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