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Name:_______________________
SID:_______________________
Section:_______________________
Final Exam -Math 022-F '07
The exam is 3 hours long. No calculators or notes are permitted. Show your
work. You do not need to simplify your answers.
Problem
Score out
of 10
1
2
3
4
5
6
7
8
9 Extra Credit
Total
Out of 90
1. It is a fact that
?
?
n=1
1
n2 =
pi2
6 .
How well does
20
?
n=1
1
n2 approximate
pi2
6 ?
2. Sketchthepolarcurve r = sin(2?)onthecoordinateaxesgivenbelow.
Find the area of one "leaf".
x
K1.5 K1.0 K0.5
0
0.5 1.0 1.5
y
K1.5
K1.0
K0.5
0.5
1.0
1.5
3. Find the area of the finite region bounded by the curves y = x2, y =
(x?2)2, and y = 0.
For the follow two problems, determine whether the series converges. Explain
your reasoning for both.
4. ?
?
n=1
e?n22
5. ?
?
n=1
parenleftbigg1
n
parenrightbiggn
6. In the coordinate axes ...

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