Explanation Let f ( x ) = x − e − x Differentiation with respect to x . f ' ( x ) = 1 + e − x To approximate the root of the equation we will use the Newton Raphson method. 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 − e − x n 1 + e − x n ........... (ii) Put n=0 in equation (ii). x 1 = x 0 − x 0 − e − x 0 1 + e − x 0 A convenient chooses for the preliminary estimation is x 0 = 1 then

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 3.8, Problem 49PS

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

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Chapter 3.8, Problem 48PS

Chapter 3.8, Problem 50PS

Chapter 3 Solutions

Calculus

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

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

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