Explanation Method used: Newton’s Method: 1. Pick an initial estimate x 0 of the root c. 2. Find a new estimate using the iterative formula x n + 1 = x n − f ( x n ) f ′ ( x n ) , n = 0 , 1 , 2 , … 3. Compute | x n − x n + 1 | . If the number is less than a prescribed positive number, then stop the iteration. The required approximation to the root x = c is x = x n + 1 . Calculation: The function is given by f ( x ) = x 5 + x − 1 . Find the derivative of f ( x ) = x 5 + x − 1 as follows. f ′ ( x ) = 5 x 4 + 1 The required iterative formula is, x n + 1 = x n − x n 5 + x n − 1 5 x n 4 + 1 = 5 x n 5 + x n − x n 5 − x n + 1 5 x n 4 + 1 = 4 x n 5 + 1 5 x n 4 + 1 By using the above mentioned Newton’s method, find x 1 at x 0 = 0.5 . x 1 = 4 ( 0.5 ) 5 + 1 5 ( 0.5 ) 4 + 1 = 1.125 1

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 11.7, Problem 14E

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To approximate: The zero of a function f(x)=x5+x−1 between x=0 and x=1 by continuing with the iteration until two successive approximations differ by less than 0.0001

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Chapter 11.7, Problem 13E

Chapter 11.7, Problem 15E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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To approximate: The zero of a function f ( x ) = x 5 + x − 1 between x = 0 and x = 1 by continuing with the iteration until two successive approximations differ by less than 0.0001

Solution Summary: The author calculates the zero of a function f(x)=x

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To approximate: The zero of a function f(x)=x5+x−1 between x=0 and x=1 by continuing with the iteration until two successive approximations differ by less than 0.0001

Want to see the full answer?

Chapter 11 Solutions