(b)Please solve the problem integration in detail.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(b)Please solve the problem integration in detail.

Solutions
(a) We apply the Integral Test and find that
np
u = x, du = 2x dx
xp
= lim
n_
boAG
1.
2e
1.
2e
= lim
2eb
Since the integral converges, the series also converges.
(b) Again applying the Integral Test,
xp
2 In x
np nə
u = In x, x = e", dx = e" du
%3D
%3D
%3D
uj 7
%3D
1.
lim
(e/2) > 1
-
%3D
%3D
b→08 In (특)
1.
The improper integral diverges, so the series diverges also.
Error Estimation
For some convergent series, such as the geometric series or the t
Example 5 of Section 9.2, we can actually find the total sum of th
can find the limiting value S of the sequence of partial sums. For mo
however, we cannot easily find the total sum. Nevertheless, we can
adding the first n terms to get sn, but we need to know how far of
sum S. An approximation to a function or to a number is more uset
panied by a bound on the size of the worst possible error that could
error bound we can try to make an estimate or approximation tha
Transcribed Image Text:Solutions (a) We apply the Integral Test and find that np u = x, du = 2x dx xp = lim n_ boAG 1. 2e 1. 2e = lim 2eb Since the integral converges, the series also converges. (b) Again applying the Integral Test, xp 2 In x np nə u = In x, x = e", dx = e" du %3D %3D %3D uj 7 %3D 1. lim (e/2) > 1 - %3D %3D b→08 In (특) 1. The improper integral diverges, so the series diverges also. Error Estimation For some convergent series, such as the geometric series or the t Example 5 of Section 9.2, we can actually find the total sum of th can find the limiting value S of the sequence of partial sums. For mo however, we cannot easily find the total sum. Nevertheless, we can adding the first n terms to get sn, but we need to know how far of sum S. An approximation to a function or to a number is more uset panied by a bound on the size of the worst possible error that could error bound we can try to make an estimate or approximation tha
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