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 x = g(xn-1), with xo = 0, will converge. What is the value of lim x,,? 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 x = g(xn-1), with xo = 0, will converge. What is the value of lim x,,? 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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![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 lim xn?
(Answer must be in 8 decimal places)
11-00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60490751-1c6c-473c-844b-470bbbb67b75%2F027194df-dae0-436e-91ea-aff34323cb8e%2Fmjidy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 lim xn?
(Answer must be in 8 decimal places)
11-00
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