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Use the Comparison Theorem to determine whether t…

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Problem 48 Hard Difficulty

(a) If $ g(x) = \frac{1}{(\sqrt{x} - 1)} $, use your calculator or computer to make a table of approximate values of $ \displaystyle \int_2^t g(x)\ dx $ for $ t = 5, 10, 100, 1000 $, and $ 10,000 $. Does it appear that $ \displaystyle \int_2^\infty g(x)\ dx $ is convergent or divergent?
(b) Use the Comparison Theorem with $ f(x) = \frac{1}{\sqrt{x}} $ to show that $ \displaystyle \int_2^\infty g(x)\ dx $ is divergent.
(c) Illustrate part (b) by graphing $ f $ and $ g $ on the same screen for $ 2 \le x \le 20 $. Use your graph to explain intuitively why $ \displaystyle \int_2^\infty g(x)\ dx $ is divergent.

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Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

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Video Transcript

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Problem

Use the Comparison Theorem to determine whether t…

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Calculus: Early Transcendentals

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

James StewartCalculus: Early Transcendentals

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Kristen Karbon

James Stewart

Calculus: Early Transcendentals