Explanation Given information: The given equation is, 4 e − x 2 sin x = x 2 − x − 1 . Calculation : Considering the function, f ( x ) = 4 e − x 2 sin x − x 2 + x + 1 . According to question it is required to find the roots of the given equation using Newton’s Method of approximation. Therefore, considering the solutions are close to x equal to 0 and 1. So applying Newton’s Method of approximation, x n + 1 = x n + f ( x n ) f ' ( x n ) When x = 0 , then x 1 = 0.2 x 2 = 0.218832730611 x 3 = 0.219163571329 x 4 = 0

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 3.8, Problem 31E

To determine

To find: The roots of the given equation 4e−x2sinx=x2−x−1 , using Newton’s Method of approximation correct to eight decimal places and sketch the graph to find initial approximations.

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Chapter 3 Solutions

Biocalculus

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The roots of the given equation 4 e − x 2 sin x = x 2 − x − 1 , using Newton’s Method of approximation correct to eight decimal places and sketch the graph to find initial approximations.

Solution Summary: The author explains how to find the roots of the given equation using Newton's Method of approximation.

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To find: The roots of the given equation 4e−x2sinx=x2−x−1 , using Newton’s Method of approximation correct to eight decimal places and sketch the graph to find initial approximations.

Chapter 3 Solutions