   Chapter 4.8, Problem 37E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Area The measurement of the side of a square floor tile is10 inches, with a possible error of 1 32 inch.(a) Use differentials to approximate the possible propagated error in computing the area of the square.(b) Approximate the percent error in computing the area of the square.

(a)

To determine

To calculate: The possible propagated error in the area of the tile.

Explanation

Given:

The side of a square tile measures 10 inches with an error of 132 inch.

Formula used:

The area of a square with each side as x is:

A(x)=x2

The propagated error is the difference between value of the function when the independent variable x is changed by a small quantity dx and the actual value of a function at x. This implies that the propagated error would be,

f(x+dx)f(x)=dy

The relative error is the ratio of the propagated error to the actual value of a function at x. This implies that the relative error would be,

f(x+dx)f(x)f(x)=dyy

The percentage error is the percentage of the propagated error to the actual value of a function at x

(b)

To determine

To calculate: The possible percentage error in the area of the tile.

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