Explanation Formula used: The Newton’s formula to find the zero of function f ( x ) is, x n + 1 = x n − f ( x n ) f ′ ( x n ) , where n = 1 , 2 , … which is often (but not always) a closer approximation to the root. The point x 2 is where the tangent line to f at x 1 crosses the x- axis. Calculation: By Newton’s formula, the value of x 2 in Newton’s method will be closer approximation to the root than the initial value of x 1 for sometimes

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

8th Edition

ISBN: 9781305279148

Author: Stewart, James, St. Andre, Richard

Publisher: Cengage Learning

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Chapter 4.8, Problem 1PT

To determine

Whether the statement “The value of x2 in Newton’s method will be closer approximation to the root than the initial value of x1” is true for sometimes, always or never.

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Chapter 4 Solutions

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Ch. 4.1 - Prob. 1PT Ch. 4.1 - Sometimes, Always, or Never: If f(c) = 0, then c...Ch. 4.1 - The critical numbers of f(x) = 3x4 = 20x3 36x2...Ch. 4.1 - Prob. 4PT Ch. 4.1 - True or False: The absolute extrema of a...Ch. 4.1 - Prob. 6PT Ch. 4.1 - Prob. 7PT Ch. 4.2 - Prob. 1PT Ch. 4.2 - Prob. 2PT Ch. 4.2 - Prob. 3PT

Ch. 4.2 - True or False: If f(x) = g(x) for all x then f(x)...Ch. 4.2 - Prob. 5PT Ch. 4.3 - Prob. 1PT Ch. 4.3 - Prob. 2PT Ch. 4.3 - Prob. 3PT Ch. 4.3 - Prob. 4PT Ch. 4.3 - Prob. 5PT Ch. 4.3 - Prob. 6PT Ch. 4.3 - True or False: If f(c) = 0, then c is a point of...Ch. 4.3 - Prob. 8PT Ch. 4.3 - Prob. 9PT Ch. 4.3 - Prob. 10PT Ch. 4.4 - Prob. 1PT Ch. 4.4 - Prob. 2PT Ch. 4.4 - Prob. 3PT Ch. 4.4 - limx(lnx)1/x= a) 0 b) 1 c) e d)Ch. 4.5 - Prob. 1PT Ch. 4.5 - Prob. 2PT Ch. 4.5 - Prob. 3PT Ch. 4.5 - True or False: If f(x) 0 for all x in an interval...Ch. 4.5 - Prob. 5PT Ch. 4.5 - Prob. 6PT Ch. 4.5 - Prob. 7PT Ch. 4.6 - Prob. 1PT Ch. 4.6 - Prob. 2PT Ch. 4.6 - Prob. 3PT Ch. 4.7 - Prob. 1PT Ch. 4.7 - A carpenter has a 10-foot-long board to mark off a...Ch. 4.7 - Prob. 3PT Ch. 4.7 - Prob. 4PT Ch. 4.8 - Prob. 1PT Ch. 4.8 - Prob. 2PT Ch. 4.8 - Prob. 3PT Ch. 4.9 - Prob. 1PT Ch. 4.9 - Prob. 2PT Ch. 4.9 - Prob. 3PT Ch. 4.9 - Prob. 4PT Ch. 4.9 - Prob. 5PT

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