   Chapter 4.8, Problem 38E 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 measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters, respectively. The possible error in each measurement is 0.25 centimeter.(a) Use differentials to approximate the possible propagated error in computing the area of the triangle.(b) Approximate the percent error in computing the area of the triangle.

(a)

To determine

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

Explanation

Given:

The altitude and base of a triangle measure 50 cm and 36 cm respectively with an error of 0.25 cm in each.

Formula used:

The formula for the area of a triangle is:

A(x)=12ab

Here, a is the altitude and b is the base.

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. This implies that the percentage error would be,

(f(x+dx)f(x)f(x))100=100dyy

Calculation:

The formula for the area of a triangle is:

A(x)=12ab

Here, a is the altitude and b is the base

(b)

To determine

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

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