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 lg'(0)| < 1, the fixed-point iteration xn = g(xn-1), with xo = 0, will converge. What is the value of lim x₂? (Answer must be in 8 decimal places) 3 11-00
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 lg'(0)| < 1, the fixed-point iteration xn = g(xn-1), with xo = 0, will converge. What is the value of lim x₂? (Answer must be in 8 decimal places) 3 11-00
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?
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Question
![Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (1) < 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 lim x?
(Answer must be in 8 decimal places)
n→∞0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e402861-6653-412b-8875-2016c7e81160%2Fa9520edc-4bd6-411d-9d5f-9c8f5e26e993%2Fomjd1mi_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (1) < 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 lim x?
(Answer must be in 8 decimal places)
n→∞0
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