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 upper limit as = 1.
The problem could also be done by
=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
lim =
1
(1 + )
lim =
(1 + 0)
lim =
1
lim = 0
Theref
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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.