If we choose po very close to the fixed point p = 3 of f(x) : 6 - the sequence (p,) of iterations of f Select an answer to p. - 2a2 - 9 If we choose po very close to the fixed point p = 3 of f(x) the sequence (p,) of - 3x iterations of f Select an answer O to p. 3r – 9 If we choose po very close to the fixed point p = 3 of f(æ) : the sequence (p,) of iterations of f select an answer to p.
If we choose po very close to the fixed point p = 3 of f(x) : 6 - the sequence (p,) of iterations of f Select an answer to p. - 2a2 - 9 If we choose po very close to the fixed point p = 3 of f(x) the sequence (p,) of - 3x iterations of f Select an answer O to p. 3r – 9 If we choose po very close to the fixed point p = 3 of f(æ) : the sequence (p,) of iterations of f select an answer to p.
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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![The image presents a mathematical problem focused on the convergence of iterations related to a function \( f(x) \) and its fixed points. Here is the transcribed content and explanation:
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- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{-x^2 - 9}{-2x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{-2x^2 - 9}{-3x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{3x^2 - 9}{2x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **Attach any explanation to your answers in the box below.**
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This problem involves understanding the behavior of sequences generated by iterating the function \( f(x) \) near its fixed points, specifically at \( p = 3 \). The task involves determining whether the sequences converge or diverge by choosing an appropriate answer for each expression, offering an opportunity to explore concepts in fixed-point iterations and convergence in numerical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64c780d2-a8a0-4ff8-a74c-59396aa6e397%2F3b80fcbd-f0ab-4f5f-94f2-f7b3cbd49bdf%2Fcxrcw7k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem focused on the convergence of iterations related to a function \( f(x) \) and its fixed points. Here is the transcribed content and explanation:
---
- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{-x^2 - 9}{-2x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{-2x^2 - 9}{-3x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **If we choose \( p_0 \) very close to the fixed point \( p = 3 \) of \( f(x) = \frac{3x^2 - 9}{2x} \), the sequence \( (p_n) \) of iterations of \( f \) [Select an answer] to \( p \).**
- **Attach any explanation to your answers in the box below.**
---
This problem involves understanding the behavior of sequences generated by iterating the function \( f(x) \) near its fixed points, specifically at \( p = 3 \). The task involves determining whether the sequences converge or diverge by choosing an appropriate answer for each expression, offering an opportunity to explore concepts in fixed-point iterations and convergence in numerical analysis.
Expert Solution
Step 1
we check the iteration are converges or not
we use |f'(x0)|<1.
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Solved in 2 steps with 1 images
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