The family f(x) = 1/xp revisited Consider the family of functions f(x) = 1/xp, where p is a real number. For what values of p does the integral exist? What is its value?
Problem 60EThe family revisited Consider the family of functions , where p is a real number. For what values of p does the integral exist What is its valueSolutionStep 1In this problem we have to find for what values of p does the integral exist.We have That is If p = 1 (i.e. p = 1), then this integral becomes Using a new variable b = 1/a, (where b goes to as a goes to 0), this limit becomes log b = , so the integral doesn’t exist. If p 1, then the integral is given by: If (i.e. p < 1), then the above limit exists and equals , whereas if the above limit is infinite (i.e. doesn’t exist). Thus the integral exists if .
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Since the solution to 60E from 7.7 chapter was answered, more than 290 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: family, its, consider, functions, integral. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “The family f(x) = 1/xp revisited Consider the family of functions f(x) = 1/xp, where p is a real number. For what values of p does the integral exist? What is its value?” is broken down into a number of easy to follow steps, and 33 words. The full step-by-step solution to problem: 60E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.