Question 17 Your answer is Blank 1. Blank 1 Add your answer 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 x, such that xn estimates the root of (x) = cos x - 3x + 1 to three significant digits? (Answer must be in 8 decimal places)
Question 17 Your answer is Blank 1. Blank 1 Add your answer 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 x, 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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![Question 17
Your answer is Blank 1.
Blank 1 Add your answer
Consider the function f(x) = cos x − 3x + 1. Since f (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 x, 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%2F6a12b9a7-0c53-4aaf-8be8-97d465226cb0%2F3f8bcfcd-16c3-42be-bc8d-54993833da12%2Fgfm0fbf_processed.png&w=3840&q=75)
Transcribed Image Text:Question 17
Your answer is Blank 1.
Blank 1 Add your answer
Consider the function f(x) = cos x − 3x + 1. Since f (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 x, 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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