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)
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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Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in
[0]. To solve f(x) = 0 using fixed-point method, we may consider the equivalent
= (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%2F60490751-1c6c-473c-844b-470bbbb67b75%2F3923a6fb-4faa-4580-b335-f7c47c46bf88%2Fta76iia_processed.jpeg&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]. To solve f(x) = 0 using fixed-point method, we may consider the equivalent
= (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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