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{\Large TEST 3

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, unless otherwise noted.
Use back of pages if necessary.
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Name \rule{5in}{.2pt}

\vspace{.2in}

\begin{enumerate}

\item  Find $\frac{dy}{dx}$ for the curve:
\[
xy^2 - \ln y = 3 - e^x
\]
\vspace{3.3in}

\item  Find the integral
\[
\int xe^{3x^2} \, dx
\]
%\vspace{3in}
\newpage

\item  Find the integral
\[
\int \frac{x-2}{x^2-4x+9} \, dx
\]
\vspace{3in}

\item  The rate of change in typing speed of the average
Utah Career College student is 
\[
\frac{dw}{dx}=\frac{6}{(x+1)^{\frac{1}{3}}}
\]
where $x$ is the number of lessons that a student has had,
and $w$ is the number of words per minute a student can type.
If $w=3$ when $x=0$ (the student can type 3 words a minute with no lessons),
find $w$ as a function of $x$.
%\vspace{3in}
\newpage

\item  Find the general solution to the differential equation:
\[
2xy \left( \frac{dy}{dx} \right) = y^2+1
\]
\vspace{4in}

\item  What is the Fundamental Theorem of Calculus, 
and what makes it fundamental?
\newpage

\item  Evaluate the integral.
\[
\int_{-1}^{3} (x^2-1) \, dx
\]
\vspace{3.5in}

\item  Tell me how to interpret your answer from the previous problem
graphically, draw the picture and explain it to me.



\end{enumerate}


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