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\fancyhead[C]{\footnotesize Quiz 3}
\fancyhead[R]{\footnotesize Fall 1997}
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%setup the questions
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\begin{document}
%\author{Alexander I.~Suciu}
\thispagestyle{plain}

\begin{center}
\bfseries 
{Prof. A. Suciu\hspace*{\fill} Name: \Blank5}\\[1pc]
{MTH 1733 % Honors Calculus 1 
\hspace*{\fill} {\Large QUIZ 3} \hspace*{\fill} Fall 1997}\\[1.5pc]
\end{center}


\begin{questions}



\item \boxed{6\text{ points}}\: 
For each of the following curves, determine the equations of 
the asymptotes, if any:
\begin{parts}
\item  $\DS{y=\frac{2}{e^x-1}+3}$
\vs
\item  $\DS{y=\ln (x^2 -4)}$
\vs
\item  $\DS{y=e^{-\DS{x^2}}}$
\end{parts}

\vs

\item \boxed{6\text{ points}}\: 
Differentiate the following functions:
\begin{parts}
\item $y=\DS{x\sqrt{\ln x}}$
\vs
\item $y=\DS{e^{\DS{e^{x^2}}}}$
\vs
\item $y=\DS{\frac{e^x+1}{x^e-1}}$
\end{parts}
\vs
\newpage

\item \boxed{8\text{ points}}\:  
Solve the following initial value problem:
\[
y''-9y=0,\quad y(0)=8,\quad y'(0)=2.
\]

\vs
\vs
\vs

\item \boxed{10\text{ points}}\:  
For each of the following non-homogeneous differential equations 
with constant coefficients, write down the \underline{general form} of 
the solution.  You may leave the undetermined coefficients of the particular 
solution \underline{unevaluated}, as in the following example.
\\[0.5pc]
$y'+y=2x+3$  \hspace*{\fill} Solution:\quad  
$y_h=C_1e^{-x}$,\quad $y_p=Ax+B$,\quad $y=y_h+y_p$.
\\
\begin{parts}
\item
$y'-3y=4x^3-5x^2$
\vs
\item
$y'-3y=e^{3x}+x+3$
\vs
\item
$y'-3y=2e^{-3x}-3e^{2x}$
\vs
\item
$y''-y'=e^{x}$
\vs
\item
$y''-y'=1$ 
\end{parts}
\vs

\end{questions}
\end{document}