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\begin{center}
\bf{MATH 120\\Exam 3\\December 4, 2002}
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1.  For which values of $r$ the function $e^{rx}$ is a solution to the differential equation $$y^{''} - y = 0$$ 

A)\ \ $r=\pm 1 \hskip.5in B)\ \  r = 1 \hskip.5in  C) \ \ r=-1 \hskip.5in   D)\ \  r=\pm2 \hskip.5in  E)\ \  r=\frac{1}{2} $ 

\pagebreak


2.  A bacteria culture grows with constant relative growth rate.  The count was 400 after 2 hours and 25,600 after 6 hours.  What was the initial
population of the culture?

\vskip.2in


A)\ \ 64 \hskip.5in B)\ \ 32 \hskip.5in  C) \ \ 25 \hskip.5in   D)\ \  50 \hskip.5in  E)\ \  100 


\pagebreak

3.  Write the fourth degree Taylor polynomial for the function $f (x) = e^{-2x}$.
\vskip.2in

$\hskip.5in A)\ \  1-2x+2x^2 - \frac{4}{3} x 3 + \frac{2}{3} x 4 \hskip.5in B) 1+2x+2x^2=\frac{4}{3} x 3 + \frac{2}{3}x 4  \hskip.5in C)  1-2x +
2x^2 -
\frac{4}{3}x 3$

$\hskip.5in  D)  1-2x+2x^2  \hskip.5in E) 1-2x$

\pagebreak



4.  Find the Taylor polynomial of degree 5 for the function $\int(x)=\sin x$.
\vskip.2in

$A)\ \  x - \frac{1}{6} x 3 \hskip.4in B)\ \  x - \frac{1}{6} x 3 + \frac{1}{120} x 5  \hskip.4in C) \ \  x + \frac{1}{6} x 3 + \frac{1}{120} x 5 
\hskip.4in D)\ \ x + \frac{1}{6} x 3  \hskip.4in  E)\ \  x + 75 x 4$

\pagebreak

5.  Calculate $ \binom{6}{3} $.

A)  \ \ 15 \hskip.5in B)\ \ 120 \hskip.5in  C)\ \ 20\hskip.5in D)\ \ 10\hskip.5in  E)\ \ 256

\pagebreak

6.  How many different committees consisting of 3 men and 2 women can be formed from 6 males and 5 females.


A) $ \ \ \binom{6}{3}  \hskip.5in B)\ \ \binom{5}{2} \hskip.5in  C)\ \ \binom{6}{3} + \binom{5}{2}\hskip.5in D)\ \
\binom{6}{3}\binom{5}{2}\hskip.5in  E)\
\ 20$

\pagebreak

7.  Suppose you toss an honest coin 5 times.  What is the probability of getting exactly 2 heads?

A) $ \ \ \binom{5}{2} (\frac{1}{2})^5 \hskip.5in B)\ \ (\frac{1}{2})^5 \hskip.5in  C)\ \ \binom{5}{2}\hskip.5in D)\ \
\binom{5}{2}+(\frac{1}{2})^5\hskip.5in  E)\
\ \binom{5}{2}(\frac{1}{3})^2(\frac{2}{3})^3$

\pagebreak

8.  Suppose that an initial amount of 1000 is invested at an annual rate of 6 percent.  Find the amount that there will be at the end of one year
if the interest is compounded quarterly.\\


A)$\ \ 1000 (1 + \frac{0.06}{4})^4\hskip.4in  B)\ \ 1000 (1 + \frac{0.06}{12})^{12} \hskip.4in  C)\ \ 1000 e^{0.06}\hskip.4in D)\ \
1200\hskip.4in E)\ \ 1000(1+\frac{6}{4})^4$

\pagebreak

9.  Use the linear approximation and estimate the size of the error for $\sqrt{4.2}$ using $f(x) = \sqrt{4+x}$.

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A)\ \ $2 + \frac{0.2}{4}, |error| \leq  \frac{(0.2)}{64}^2$

B)\ \ $2 - \frac{0.2}{4} , |error| \leq \frac{(0.2)}{64}^2$

C)\ \ $2 + \frac{4.2}{4} , |error| \leq \frac{(4.2)}{32}^2$

D)\ \ $2 , |error| \leq 0.2$

E)\ \ No Solution

\pagebreak

10.  Find 

\hskip.5in $\displaystyle \sum_{k=o}^\infty\ \  \frac{8}{5^k}$

\vskip.2in

A)$\ \ 10 \hskip.8in B)\ \ 5  \hskip.8in  C)\ \ \frac{5}{4} \hskip.8in D)\ \ 8 \hskip.8in E)\ \ \frac{8}{5}$ 

\vskip7in You're Done!!!!!




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