MATH 101 HOMEWORK 6
Due on Wednesday, October 22
Covers sections 6.5 and 6.6. For full credit, show all work.
1. (12 marks, 4 for each part) For each of the following integrals, use the comparison test
to determine whether it is convergent of divergent. (Do not try to compute the integrals:
this could be either very hard or impossible.)
Z
∞
(a)
1
Z
∞
(b)
√
x3 − 1
dx,
x2 + 1
(x2 + 1)e−x dx,
2
0
Z
(c)
0
∞
dx
.
+ x3
x1/3
Z
1
2
ex dx.
2. (8 marks) We want to evaluate numerically the integral
0
(a) Write out (but do not try to evaluate) the midpoint and trapezoid approximations M4
and T4 .
(b) How large should n be, if we want the error for the midpoint approximation Mn to be
no greater than .001? (Feel free to use a calculator.)
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