MTH 1002 Calculus II Fall ’07
11/30/’07 Practice make up test
1. Find the radius and interval of convergence for the series
∞
X
k=0
(−1)kxk
k!. Show
that the McLaurin series for e−xconverges to the given series.
Hint: Find McLaurin series expansion for e−xand use remainder theorem to
show the convergence..
2. Using alternating series test to show that
∞
X
k=2
(−1)k
kln kconverges. Using the inte-
gral test check the conditional convergence of the given series.
3. Evaluate Z∞
0
5
x2+x−2dx.
4. Find the volume of the solid generated by revolving x= sin2yabout x = 1
between 0 and π
2.
5. Find the area of the surface generated when the curve y=x2from x= 0 to
x= 1 is revolved about x-axis.
6. Find the area of the region enclosed by y= ln x,x=eand the x-axis.
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