Plotting the curves = 2 2 , = 2 and = 0, we have
We first find the area shaded in blue.
For limits:
2 2 = 2
2 2 = 2
= 1
We take the lower limit as = 0 since it is a constraint in the question and the
=1
+1
2
Divergence test
The divergence test says that if limit of a sequence is not zero or does not exist, the sum diverges.
Here
=
+1
2
lim = lim
+1
2
1
(1 + )
lim = lim
2
1
(1 + )
lim = lim
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Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
5. [a] Calculate the sum of the rectangular areas in Fig. 241
[h] From part (a],wha1 can we 5a,r ahnut the area of u:
ahadad Region in Fig.14h?
03(3) +66%)
3 + :2 =5
3) M Emld (63100 IS <5 '00?
>1
QUIZ # 5 Solution Key
Math 141/6380, Due 11:59PM, Sunday, July 2, 2017
1. Find the partial fraction decomposition for the rational function
Solution: Assume that
2x2 x 4
x3 4x
2 x 2 x 4 2 x 2 x 4 A Bx
QUIZ # 1 Solution Keys
Math 141/6380, Due 11:59PM, Sunday, June 4, 2017
1. The velocity of a car after t seconds is 20 2 feet per second. (a) How many seconds
does it take for the car to come to a sto