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Explain why or why not Determine whether the | Ch 7.7 - 47E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 47E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 47E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. If f is continuous and 0 < f(x)< g(x) on the interval \([0, \infty)\) and \(\int_{0}^{\infty} g(x) d x=M<\infty\) then \(\int_{0}^{\infty} f(x) \ d x\) exists

b. If \(\lim _{x \rightarrow \infty} f(x)=1\), then \(\int_{0}^{\infty} f(x) \ d x\) exists.

c. If \(\int_{0}^{1} x^{-p} \ d x\) exists, then \(\int_{0}^{1} x^{-q} \ d x\) exists, where q > p.

d. If \(\int_{1}^{\infty} x^{-p} \ d x\) exists, then \(\int_{1}^{\infty} x^{-q} \ d x\) exists, where q > p.

e. \(\int_{1}^{\infty} \frac{d x}{x^{3 p+2}}\) exists for \(p>-\frac{1}{3}\)

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Chapter 7.7, Problem 47E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The full step-by-step solution to problem: 47E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “?Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. If f is continuous and 0 < f(x)< g(x) on the interval \([0, \infty)\) and \(\int_{0}^{\infty} g(x) d x=M<\infty\) then \(\int_{0}^{\infty} f(x) \ d x\) existsb. If \(\lim _{x \rightarrow \infty} f(x)=1\), then \(\int_{0}^{\infty} f(x) \ d x\) exists.c. If \(\int_{0}^{1} x^{-p} \ d x\) exists, then \(\int_{0}^{1} x^{-q} \ d x\) exists, where q > p.d. If \(\int_{1}^{\infty} x^{-p} \ d x\) exists, then \(\int_{1}^{\infty} x^{-q} \ d x\) exists, where q > p.e. \(\int_{1}^{\infty} \frac{d x}{x^{3 p+2}}\) exists for \(p>-\frac{1}{3}\)” is broken down into a number of easy to follow steps, and 100 words. This full solution covers the following key subjects: exists, Where, give, Continuous, explain. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 47E from 7.7 chapter was answered, more than 389 students have viewed the full step-by-step answer.

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Explain why or why not Determine whether the | Ch 7.7 - 47E