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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

A window has the shape of a square surmounted by a semicircle. The base of the window is measured ns having width 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.

To determine

To estimate: The maximum error in the area of the window.

Explanation

Given:

Let l be the width of the window with 60 cm. That is, l=60.

The error in measurement of 0.1 cm is dl=0.1.

Formula used:

The area of square with radius r is, A=r2.

The area of semicircle with radius r is,  B=12πr2.

Calculation:

The area of the window is computed as follows,

C(l)={area of the square with radius l}+{area of the semicircle with radius l2}=l2+12π(l2)2

Obtain the derivative C(l)

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