1. Consider the function f(x) = x² - sin(x) -0.5. Plot the graph of the function in the interval [0, 4]. 2. Let g1(x) = = sin(x) +0.5 Is the g1(x) satisfied the condition of convergence at initial guess 3 x xo=1? Explain your answer. 3. Use g1(x) and initial guess in step 2 to find the root of the function f(x). Perform 10 iterations of the Fixed-point method. 4. Understand the Fixed-point method to write the algorithm.
1. Consider the function f(x) = x² - sin(x) -0.5. Plot the graph of the function in the interval [0, 4]. 2. Let g1(x) = = sin(x) +0.5 Is the g1(x) satisfied the condition of convergence at initial guess 3 x xo=1? Explain your answer. 3. Use g1(x) and initial guess in step 2 to find the root of the function f(x). Perform 10 iterations of the Fixed-point method. 4. Understand the Fixed-point method to write the algorithm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![1. Consider the function f(x) = x² – sin(x) – 0. 5. Plot the graph of the function in the
interval [0, 4].
2. Let g1(x):
=
sin(x) +0.5
Is the g1(x) satisfied the condition of convergence at initial guess
5
x
xo=1? Explain your answer.
3. Use gl (x) and initial guess in step 2 to find the root of the function f(x). Perform 10 iterations
of the Fixed-point method.
4.
Understand the Fixed-point method to write the algorithm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F429ffdfb-db8b-4178-8c86-86285a2be835%2F89644e23-e007-4bff-b16c-4966e5890b36%2Fz686r9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the function f(x) = x² – sin(x) – 0. 5. Plot the graph of the function in the
interval [0, 4].
2. Let g1(x):
=
sin(x) +0.5
Is the g1(x) satisfied the condition of convergence at initial guess
5
x
xo=1? Explain your answer.
3. Use gl (x) and initial guess in step 2 to find the root of the function f(x). Perform 10 iterations
of the Fixed-point method.
4.
Understand the Fixed-point method to write the algorithm.
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