The function f(x) = Tx describes the area of a circle, f(x), in square inches, whose radius measures x inches a. If the radius is changing. find the average rate of change of the area with respect to the radius as the radius changes from 3 inches to 3.2 inches and from 3 inches to 3.02 inches. b. If the radius is changing, find the instantaneous rate of change of the area with respect to the radius when the radius is 3 inches. a. As the radius changes from 3 inches to 3.2 inches, the average rate of change of the area with respect to the radius is square inches per inch, (Simplify your answer. Type an exact answer, using a as needed. Use integers or decimals for any numbers in the expression.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
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The function f(x) = TX describes the area of a circle, f(x), in square inches, whose radius measures x inches.
%3D
a. If the radius is changing, find the average rate of change of the area with respect to the radius as the radius changes from 3 inches to 3.2 inches and from 3 inches to 3.02 inches.
b. If the radius is changing, find the instantaneous rate of change of the area with respect to the radius when the radius is 3 inches.
a. As the radius changes from 3 inches to 3.2 inches, the average rate of change of the area with respect to the radius is
(Simplify your answer. Type an exact answer, using t as needed. Use integers or decimals for any numbers in the expression.)
square inches per inch.
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Transcribed Image Text:The function f(x) = TX describes the area of a circle, f(x), in square inches, whose radius measures x inches. %3D a. If the radius is changing, find the average rate of change of the area with respect to the radius as the radius changes from 3 inches to 3.2 inches and from 3 inches to 3.02 inches. b. If the radius is changing, find the instantaneous rate of change of the area with respect to the radius when the radius is 3 inches. a. As the radius changes from 3 inches to 3.2 inches, the average rate of change of the area with respect to the radius is (Simplify your answer. Type an exact answer, using t as needed. Use integers or decimals for any numbers in the expression.) square inches per inch. Enter your answer in the answer box and then click Check Answer. Clear All parts remaining P Type here to search )耳
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It is given that, the functionf(x)=πx2   ,  where f(x) is area of circle and x is the radius of circle.And radius changes from 3 inches to 3.2 inches.we have to find the average rate of change of the area w.r.t the radius.

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