Explanation Let f ( x ) = x − cos x Differentiation with respect to x . f ' ( x ) = 1 + sin x To approximate the root of the equation we will use the Newton Raphson method. Since | cos x | ≤ 1 then we have that | x | ≤ 1 . We know Newton Raphson method x n + 1 = x n − f ( x n ) f ' ( x n ) ........... (i) Hence we can write x n + 1 = x n − x n − cos x n 1 + sin x n .......... (ii) Put n=0 in equation (ii). x 1 = x 0 − x 0 − cos x 0 1 + sin x 0 A convenient chooses for the preliminary estimation is x 0 = 1 then

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.8, Problem 48PS

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Chapter 3.8, Problem 47PS

Chapter 3.8, Problem 49PS

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Chapter 3 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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To estimate the root of the equation cos x = x with the help of Newton Raphson method.

Solution Summary: The author explains how to estimate the root of the equation mathrmcosx=x using the Newton Raphson method.

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Chapter 3 Solutions