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 4 − 50 . Find the derivative of f ( x ) = x 4 − 50 as follows. f ′ ( x ) = 4 x 3 The required iterative formula is, x n + 1 = x n − x n 4 − 50 4 x n 3 = 4 x n 4 − x n 4 + 50 4 x n 3 = 3 x n 4 + 50 4 x n 3 By using the above mentioned Newton’s method, find the three iterations for the function f ( x ) = x 4 − 50 at x 0 = 2.5

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.7, Problem 6E

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To estimate: The value of a radical 504 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x0=2.5 for the function f(x)=x4−50.

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Chapter 11.7, Problem 5E

Chapter 11.7, Problem 7E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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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 estimate: The value of a radical 50 4 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x 0 = 2.5 for the function f ( x ) = x 4 − 50 .

Solution Summary: The author calculates the value of a radical sqrt[4]50 to five decimal places by using three iterations of Newton's method.

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To estimate: The value of a radical 504 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x0=2.5 for the function f(x)=x4−50.

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Chapter 11 Solutions