Explanation Given: f is a linear function. Formula used: Newton method: x n + 1 = x n − f ( x n ) f ′ ( x n ) Calculation: Newton’s method is used to find the location of a root by using the linear approximation of a function. Let f ( x ) is a linear function. So, f ( x ) = a x + b . Now, find the derivative of the function. f ′ ( x ) = a By the formula of Newton’s method. x 1 = x 0 − f ( x 0 ) f ′ ( x 0 ) = x 0 − a x 0 + b a Simplify the above equation. x 1 = x 0 − a x 0 a − b a = x 0 − x 0 − b a = − b a Now, find the value of x n + 1

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.7, Problem 1PQ

To determine

Write how many iterations of Newton’s Method are required to compute a root if f is a linear function.

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Chapter 4.6, Problem 82E

Chapter 4.7, Problem 2PQ

Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY

Write how many iterations of Newton’s Method are required to compute a root if f is a linear function.

Solution Summary: The author explains how Newton's method is used to find the location of a root.

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Write how many iterations of Newton’s Method are required to compute a root if f is a linear function.

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Chapter 4 Solutions