Chapter 6.1, Problem 82E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Euler’s Method Compare the values of the approximations in Exercises 79–81 with the valuesgiven by the exact solution. How does the error change as increases?

To determine
How the error change as h increases.

Explanation

Given:

 x 0 0.2 0.4 0.6 0.8 1 y(x) (exact) 0 0.22 0.4801 0.7807 1.1231 1.5097 y(x) (h = 0.2) 0 0.2 0.436 0.7074 1.014 1.3561 y(x) (h = 0.1) 0 0.2095 0.4568 0.7418 1.0649 1.4273

Explanation:

At x = 0.2, the exact solution is y(x)= 0.2200, and the approximate solutions are

y(x) = 0.2095, when h = 0.1

y(x) = 0.2000, when h = 0.2

Using,

%error=|y(x)approximatey(x

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