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{\Large TEST 1

Math 129 - R5}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
\vspace{.1in}

Name \rule{5in}{.2pt}

\vspace{.2in}

\begin{enumerate}

\item  Find the limit:
\[
\lim_{x \ra 3} \frac{x^2+x-12}{x-3}
\]
\vspace{2in}

\item  
Can you fill in the question mark (?) to make the following function 
continuous? 
If you can, fill in the (?) and tell me why that makes the function
continuous.
If not, explain why not.
\[
g(x)=\left\{
\begin{array}{cr}
\frac{x^2+x-12}{x-3} & x \neq 3 \\
? & x = 3 \\
\end{array}
\right.
\]
\newpage
%\vspace{2in}

\item  Using the limit definition of derivative, find $\frac{dy}{dx}$
for $y=4x^2-2x$.
\vspace{4in}

\item The percentage of high school seniors who have tried pot can be
modeled by the formula with the function
\[
M(t)=-.2286t^2 + 37.07t - 1444.41
\]
Where $t$ is the number of years past 1900.
\begin{enumerate}
\item  \label{75} Find $M'(75)$
\vspace{2.3in}
\item  Write a good sentence that would explain to someone who
did not understand calculus what your answer in part~\ref{75} means.
\end{enumerate}
%\vspace{3in}
\newpage

\item  Find $\frac{dy}{dx}$, do not simplify:
\[
y=\frac{3x^2-5}{6x-7x^3}
\]
\vspace{3.8in}

\item  For the function below, find $A'(4)$:
\[
A(x)=\left( x^{3}+\frac{64}{x^2}+2 \right) 
\left(\frac{16}{\sqrt{x}}-3x \right)
\]
%\vspace{3in}
\newpage

\item  For the given function below, find the slope of the tangent line
at the point $(2,3)$:
\[
y = \sqrt{x^3+1}
\]
\vspace{3.5in}

\item  The typing speed of a secretary student at Utah Career College 
(in words per minute) can be modeled by the function:
\[
S= 10 \sqrt{0.8t+4}
\]
Where $t$ is the number of hours training he or she has had.
Find the rate at which his or her speed is changing and what does this 
rate mean when the student has had 10 hours training.
%\vspace{3in}
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\end{enumerate}


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