MIDTERM 1
Math 1320 sec 004
October 4. 2013
Name:
by writing my name
I
sar b the hocede
Read all of the following information before starting the exam:
Show all work, clearly and in order, if you want to get full credit. I may take off points if
I canilot see how you arrived at your answer (even if your final answer is correct).
• No calculators or books are allowed for this test.
• You may use a flowchart you have created that describes series convergence tests. You
cannot use one you have not created or has more information than series convergence tests.
• Please keep your written answers brief; be clear and to the point. You may lose points for
incorrect or irrelevant statements.
• Please turn off celiphones, turn hats backwards, take out headphones and sit every other
seat, if possible.
• You have 50 minutes to work on this exam.
o
Good luck!
Page (value)
1 (20 points)
2 (20 points)
3 (15_points)
4_(20_points)
Total (75 points)
Score
(20 points) Short Answer. For True or False you must write ‘True’ or ‘False’ and justify
your answer to receive credit.
dx represents the volume generated
)
2
r(1 .r
True or False. The integral
a. ( pts)
2
and p 0 about the p-axis.
b rotating the region enclosed by y 1
1.
f’
...
b.
(
pts)
...
Write down the solution to the differential equation
kP with P(0)
=
Po.
t
A fish farmer has 5000 catfish in his pond. The number of catfish increases
pts)
by 8Vc per month and the farmer harvests 300 catfish each month. l\rrite down a recursive
relationship that shows the catfish population P after n months.
c.
(.
d.
(
pts)
If
f(x)
=
Z
write down a series that represents
.
A computer controlled router is used to cut designs into table tops. The
e. ( pts)
consists of a parametric curve given by x(t) = e + e, y(t) = 5 2t for
today
design being cut
0 < t < 3 where x and y are in units of cm. Set up, but do not evaluate, an integral representing
the length of this curve.
—
2. (12 points) Determine if the following series converge or diverge and give a short reason
for your answer.
(
pts)
b.
(
pts)
c.
(
pts)
a.
3.
Z
n=1
2n+1
in(/4)
Z()’
1
I
(8 points)
a. (8 pts)
What is the interval of convergence for the power series
I
-
-•
Z
n(x±2
3+1
4. (15 poinis)
a. (7 pts)
2 +
Solve the differential equation (g
ry2)
1
x
=
is given by the equation
The solution to the differential equation
b. (3 pts)
= x
3 + C. We are given the initial condition y(O) = 2. Find C.
An apple pie comes out of the oven at 150 degrees Fahrenheit and is put in a
room with constant tempel ature of 75 degrees Fahrenheit Using Newton’s Law of Cooling we
find a solution for the temperature, T, of the pie to be
c. (5 pts)
T(t)
=
75 + 75e
where t is measured in hours. After 1 hour the pie has cooled to 100 degrees Fahrenheit. Find
k.
5.
(20 points)
A spring has a natural length of 20 cm. If a 25 Newton force is required to
a. (8 pts)
keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to
25 cm?
1oc
2
2O
/
(
‘C
b. (8 pts) The velocity of blood flowing through a blood vessel with radius R and lenght
1 at a distance r from the central axis is
v(r)
2
(R
=
—
)
2
r
where P is the pressure difference between the ends of the vessel and m is the viscosity of blood.
Find the average velocity (with respect to r) over the interval 0 < r < R.
f
/
r
U
j?
/
1
—
j-.:
L
I
ti1S
-
c. ( pts)
Use the niethod of cylindrical shells to set up an integral that represents the
volume of the solid generated by rotating the region enclosed by the curves y =
y = 0 and
x = 1 about the y-axis. Do not evaluate this integral.
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