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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm.

(a) Use differentials to estimate the maximum error in the calculated area of the disk.

(b) What is the relative error? What is the percentage error?

(a)

To determine

To estimate: The maximum error in the calculated area of circular disk.

Explanation

Given:

The radius of the circular disk is 24 cm and the maximum error in measurement is 0.2 cm.

Calculation:

Suppose r be a radius of the circle.

Note that, the area of the circular disk is S=πr2.

The differential is dS=f(r)dr (1)

Derivative of the function f(r)=πr2 is f(r)=2πr,

Substitute f(r)=2πr in equation (1),

(b)

To determine

To find: The relative error and percentage error.

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