\documentclass{exam}[12pt]

\usepackage{amsfonts,amsmath}

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\begin{document}
\pagestyle{head}

\firstpageheader{\large Calculus I}{\bf\Large Differentials}{\large Name:\hspace{1in} }
%\extraheadheight{.7in}
%\extrafootheight{-1in} 
%\small{\textit{Work all questions completely.  Show all work.}}

\begin{questions}
\large{


\question Find $dy$ if $y = x\csc(3x^2-1)$.
\vspace{1.4in}

\question Find $ds$ if $s = -16 t^2 + 5 t +100$.
\vspace{1.4in}

\question Find $dx$ if $y = \dfrac{\sin{2x}}{1-\log_3{x^2}}$.
\vspace{2.3in}


\question Use differentials to approximate $(3.02)^2 - 4(3.02)+2$.
\vspace{2in}

\pagebreak

\question The crew of Pigs in Space discover a giant cube floating in space.
Their sensors report that the sides of cube are 300 m long, but they know from
several previous unfortunate incidents, that their sensors are only accurate
to within 3\%.  What is the approximate error and the percentage error in
their measurement of the volume of the cube?
\vspace{2.5in}

\question The strange cube suddenly begins to contract.  If the sides are
shrinking at 2 m/sec, at what rate is the volume changing when the
sides are 270 m long?

%\vspace{2.5in}
%\question Consider the function $f(x)=x^3 - 6x^2$ on the interval $[-1,5]$.
% Find all critical values and find the absolute max and min.

}
\end{questions}
\end{document}