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 x₂ = g(xn-1), with xo = 0, will converge. What is the value of x, 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 x₂ = g(xn-1), with xo = 0, will converge. What is the value of x, 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.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ(x) has a root in
[0, 1] 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(x₂-1), with x = 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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e402861-6653-412b-8875-2016c7e81160%2F16153b98-a064-4b01-be6a-dac8cbd0c93f%2Fbgkgbx_processed.png&w=3840&q=75)
Transcribed Image Text:-
Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ(x) has a root in
[0, 1] 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(x₂-1), with x = 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)
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