Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, f (x) has a root in [0]. To solve f(x) = 0 using fixed-point method, we may consider the equivalent equation x = (1 + cos x). Let g(x) = (1 + cos x). Since |g'(0)| < 1, the fixed-point iteration xn= g(xn-1), with xo = 0, will converge. What is the value of xn such that xn estimates the root of (x) = cos x - 3x + 1 to three significant digits? (Answer must be in 8 decimal places)

Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, f (x) has a root in [0]. To solve f(x) = 0 using fixed-point method, we may consider the equivalent equation x = (1 + cos x). Let g(x) = (1 + cos x). Since |g'(0)| < 1, the fixed-point iteration xn= g(xn-1), with xo = 0, will converge. What is the value of xn such that xn estimates the root of (x) = cos x - 3x + 1 to three significant digits? (Answer must be in 8 decimal places)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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