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\textbf{Name:}$\underline{\hspace{3in}}$\\
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\textbf{Pledged:}$\underline{\hspace{3in}}$
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Rhodes College
\par
Math 115: Applied Calculus
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Module 2 Exam
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October 10, 2008
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\begin{tabular}{|c | c | c |}
\hline \ \ Problem\ \  & \ \ \ Points\ \ \  & \ \ \ Score\ \ \ \\
\hline 1 & 20 & \\
\hline 2a & 10 & \\
\hline 2b & 10 & \\
\hline 2c & 10 & \\
\hline 2d & 10 & \\
\hline 2e & 10 & \\
\hline 3a & 15 & \\
\hline 3b & 15 & \\
\hline Total & 100 & \\
\hline
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\noindent \textbf{SHOW ALL WORK.} May the force be with you.

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\begin{enumerate}

% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX  Problem 1

\item (20 points)
Determine the derivative of
\[
        f(x)    =   \frac{3}{x}
\]
directly from the (limit) definition; i.e. the ``Three-Step Method."  {\bf Show your work.}

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% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX  Problem 2

\item (50 points)
Find the derivative of each of the following functions.  You may use
any of the shortcuts we have studied.  You are encouraged {\bf not}
to simplify your answers.  Really.  Take the derivative.  That's all.

{\bf a.} (10 points)

{\LARGE
$f(x) = 3x^7 - 5\sqrt{x}$
}

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{\bf b.} (10 points)

{\LARGE
$g(x) = \frac{2}{\sqrt[5]{x}} + \frac{5}{x^3}$
}

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{\bf c.} (10 points)

{\LARGE
$G(t) = e^x \sin (2x)$
}

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{\bf d.} (10 points)

{\LARGE
$F(x) = 7e^{x^2 - 13 x - 11}$
}

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{\bf e.} (10 points)

{\LARGE
$\Gamma (x) = \frac{\cos x + 4e^x}{\ln x}$
}





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% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX  Problem 3

\item (30 points)
Find an equation of the tangent line to each curve at the point $(a,
f(a))$.


{\bf a.} (15 points)

$f(x) = 5^x$ with $a = 4$

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{\bf b.} (15 points)

$f(x) = x^4 + 3x^2 + 1$ with $a = 5$





\end{enumerate}

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