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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 47e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 47e

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

ISBN: 9780321570567 2

## Solution for problem 47E Chapter 7.7

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 $$p>-\frac{1}{3}$$

Step-by-Step Solution:
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##### 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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