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 2 − 3 . Find the derivative of f ( x ) = x 2 − 3 as follows. f ′ ( x ) = 2 x The required iterative formula is, x n + 1 = x n − x n 2 − 3 2 x n = 2 x n 2 − x n 2 + 3 2 x n = x n 2 + 3 2 x n By using the above mentioned Newton’s method, find the three iterations for the function f ( x ) = x 2 − 3 at x 0 = 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 1E

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To estimate: The value of a radical 3 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x0=1.5 for the function f(x)=x2−3.

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Chapter 11.7, Problem 3CQ

Chapter 11.7, Problem 2E

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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. Find a bound in the error...Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - According to a joint study conducted by Oxnards...Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Prob. 1CQ Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - In Exercises 1021, find the nth term of the...Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.3 - Prob. 1CQ Ch. 11.3 - Prob. 2CQ Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Suppose that a dose of C units of a certain drug...Ch. 11.3 - Prob. 44E Ch. 11.3 - In Exercises 4548, determine whether the statement...Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.4 - Prob. 1CQ Ch. 11.4 - Prob. 2CQ Ch. 11.4 - Prob. 3CQ Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 50E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 53E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Prob. 56E Ch. 11.4 - Prob. 57E Ch. 11.4 - Prob. 58E Ch. 11.4 - Prob. 59E Ch. 11.4 - Prob. 60E Ch. 11.5 - Prob. 1CQ Ch. 11.5 - a. What is the radius of convergence of a power...Ch. 11.5 - Prob. 3CQ Ch. 11.5 - Prob. 4CQ Ch. 11.5 - Prob. 5CQ Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Prob. 5E Ch. 11.5 - Prob. 6E Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Prob. 28E Ch. 11.5 - Prob. 29E Ch. 11.5 - Prob. 30E Ch. 11.5 - Prob. 31E Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.5 - Prob. 35E Ch. 11.5 - Prob. 36E Ch. 11.6 - Prob. 1CQ Ch. 11.6 - Prob. 2CQ Ch. 11.6 - Prob. 3CQ Ch. 11.6 - Prob. 1E Ch. 11.6 - Prob. 2E Ch. 11.6 - Prob. 3E Ch. 11.6 - Prob. 4E Ch. 11.6 - Prob. 5E Ch. 11.6 - Prob. 6E Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Prob. 9E Ch. 11.6 - Prob. 10E Ch. 11.6 - Prob. 11E Ch. 11.6 - Prob. 12E Ch. 11.6 - Prob. 13E Ch. 11.6 - Prob. 14E Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 16E Ch. 11.6 - Prob. 17E Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 20E Ch. 11.6 - Prob. 21E Ch. 11.6 - Prob. 22E Ch. 11.6 - Prob. 23E Ch. 11.6 - Prob. 24E Ch. 11.6 - Prob. 25E Ch. 11.6 - Prob. 26E Ch. 11.6 - Prob. 27E Ch. 11.6 - Prob. 28E Ch. 11.6 - Prob. 29E Ch. 11.6 - Prob. 30E Ch. 11.6 - Prob. 31E Ch. 11.6 - Prob. 32E Ch. 11.7 - Prob. 1CQ Ch. 11.7 - Prob. 2CQ Ch. 11.7 - Prob. 3CQ Ch. 11.7 - Prob. 1E Ch. 11.7 - Prob. 2E Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Prob. 5E Ch. 11.7 - Prob. 6E Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Prob. 11E Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Prob. 15E Ch. 11.7 - Prob. 16E Ch. 11.7 - Prob. 17E Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Prob. 20E Ch. 11.7 - Prob. 21E Ch. 11.7 - Prob. 22E Ch. 11.7 - In Exercises 2328, make a rough sketch of the...Ch. 11.7 - Prob. 24E Ch. 11.7 - Prob. 25E Ch. 11.7 - Prob. 26E Ch. 11.7 - Prob. 27E Ch. 11.7 - Prob. 28E Ch. 11.7 - Prob. 29E Ch. 11.7 - Prob. 30E Ch. 11.7 - Prob. 31E Ch. 11.7 - Prob. 32E Ch. 11.7 - Prob. 33E Ch. 11.7 - Prob. 34E Ch. 11.7 - Prob. 35E Ch. 11.7 - Prob. 36E Ch. 11.7 - Prob. 37E Ch. 11.7 - Prob. 38E Ch. 11.7 - Prob. 39E Ch. 11.7 - Prob. 40E Ch. 11.7 - Prob. 41E Ch. 11.7 - Prob. 1TE Ch. 11.7 - Prob. 2TE Ch. 11.7 - Prob. 3TE Ch. 11.7 - Prob. 4TE Ch. 11.7 - Prob. 5TE Ch. 11.7 - Prob. 6TE Ch. 11.7 - Prob. 7TE Ch. 11.7 - Prob. 8TE Ch. 11 - Prob. 1CRQ Ch. 11 - Prob. 2CRQ Ch. 11 - Prob. 3CRQ Ch. 11 - Prob. 4CRQ Ch. 11 - Prob. 5CRQ Ch. 11 - Prob. 6CRQ Ch. 11 - Prob. 7CRQ Ch. 11 - Prob. 8CRQ Ch. 11 - Prob. 9CRQ Ch. 11 - Prob. 10CRQ Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - In Exercises 21 and 22, find the sum of the...Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Prob. 42RE Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 1BM Ch. 11 - Prob. 2BM Ch. 11 - Determine whether the series converges or...Ch. 11 - Prob. 4BM Ch. 11 - Prob. 5BM

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To estimate: The value of a radical 3 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x 0 = 1.5 for the function f ( x ) = x 2 − 3 .

Solution Summary: The author calculates the value of a radical sqrt3 to five decimal places using three iterations of Newton's method.

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To estimate: The value of a radical 3 to five decimal places by using three iterations of Newton’s method with the indicated initial guess x0=1.5 for the function f(x)=x2−3.

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Chapter 11 Solutions