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Regions bounded by exponentials Let a > 0 and let R be the
Chapter 7, Problem 59E(choose chapter or problem)
Regions bounded by exponentials Let a > 0 and let R be the region bounded by the graph of \(y=e^{-a x}\) and the x-axis on the interval \([b, \infty)\) .
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?
Questions & Answers
QUESTION:
Regions bounded by exponentials Let a > 0 and let R be the region bounded by the graph of \(y=e^{-a x}\) and the x-axis on the interval \([b, \infty)\) .
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?
ANSWER: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: ”