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Regions bounded by exponentials Let a > 0 and let R be the

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

Solution for problem 59E 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 59E

Regions bounded by exponentials Let a > 0 and let R be the region bounded by the graph of y = e?ax and the x-axis on the interval [b, ?).a. Find A(a, b). the area of R as a function of a and b.________________b. Find the relationship b = g(a)such that A(a, b)=2.________________c. What is the minimum value of b (call it b*)such that when b > b*, A(a, b)= 2 for some value of a > 0?

Step-by-Step Solution:

Problem 59ERegions bounded by exponentials Let a > 0 and let R be the region bounded by the graph of and the x-axis on the interval [b, ).a. Find A(a, b). the area of R as a function of a and b.b. Find the relationship b = g(a)such that A(a, b)=2.c. What is the minimum value of b (call it b*)such that when b > b*, A(a, b)= 2 for some value of a > 0SolutionStep 1In this problem we have to find the area of the region bounded by the graph of and the x-axis on the interval [b, ).We shall find the area by the following method. “If f(x) is a continuous and nonnegative function of x on the closed interval [a, b], then the area of the region bounded by the graph of f, the x-axis and the vertical lines x=a and x=b is given by: ”

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Chapter 7.7, Problem 59E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Regions bounded by exponentials Let a > 0 and let R be the