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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 xn such that xn
estimates the root of (x) = cos x - 3x + 1 to three significant digits? (Answer must be
in 8 decimal places)
our answer is Blank 1.
Blank 1 Add your answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e3f0ad9-94f2-4143-8db2-49e17c476286%2Fdee8bd61-b653-49dd-b710-b068bb570910%2Ff5fecrl_processed.png&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 xn such that xn
estimates the root of (x) = cos x - 3x + 1 to three significant digits? (Answer must be
in 8 decimal places)
our answer is Blank 1.
Blank 1 Add your answer
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