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\begin{document}
%\author{Alexander I.~Suciu}
%\centerline{MTH 1733 --- Quiz \#1 --- Fall 1997}

Prof. A. Suciu \hfil{Name: \Blank5}
\bigskip
\ \
\centerline{\large MTH 1733 --- Honors Calculus 1 --- Fall 1997}

\bigskip
\centerline{\Large\bfseries Quiz 1}
\medskip

In Problems $1$ and $2$, $H$ is infinite, $\e$ is (a non-zero) 
infinitesimal, and $x$ is standard.

\begin{enumerate}
\item Tell whether each of the following expressions is 
infinitesimal, moderate, or infinite.

\begin{enumerate}
\item  $\DS{\frac{\e - 2}{\e^2}}$

\vskip 0.7 in
\item  $\DS{\frac{\e^2 - \DS{\frac{1}{\e}}}{\e^2+\DS{\frac{1}{\e}}}}$

\vskip 0.7 in
\item  $\DS{\frac{\sqrt{H^2+1}}{3H-2}}-\frac{1}{2}$

\vskip 0.7 in
\item  $\DS{\frac{5H+6}{H^2+3H+2}}$
\end{enumerate}

\vskip 0.7 in
\item Find the standard parts of each of the following numbers.

\begin{enumerate}
\item  $\DS{\frac{\DS{\frac{2}{x+\e}-\frac{2}{x}}}{\e}}$

\vskip 0.7 in
\item  $\DS{\frac{(H+1)^2-5}{H^2+2H+1}}$

\vskip 0.7 in
\item  $\DS{\frac{27 - (3+\e)^3}{\e}}$
\end{enumerate}

\newpage 

\item Determine whether the following functions are differentiable at the 
indicated point (using the definition of the derivative).  If differentiable, 
calculate the derivative at that point.

\begin{enumerate}
\item  $f(x) = \DS{\frac{1-|x|}{1+|x|}}$ at $x=0$
\vskip 1 truein
\item  $f(x) = x|x^3 - 2|$ at $x=0$
\end{enumerate}

\vskip 1 truein

\item Find the derivatives of the following functions:

\begin{enumerate}
\item  $y=\DS{\frac{1}{2}x^4 + \frac{2}{5}}$

\vskip 1 truein

\item  $y=\DS{\sqrt{x^3} - \DS{\frac{1}{\sqrt{x}}}}$ 
\end{enumerate}

\vskip 1 truein

\item  Let $f(x)=x^2-3x+1$. 

\begin{enumerate} 
\item Find the equation of the tangent line to the graph $y=f(x)$ 
at the point where $x=2$.

\vskip 1.5 truein

\item  At what point on the graph $y=f(x)$ is the tangent 
line parallel to the line $y=7x-6$?
\end{enumerate}

\end{enumerate}

\end{document}