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4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 x 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?

4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 x 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?

Advanced Engineering Mathematics
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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4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 × 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?
Transcribed Image Text:4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 × 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?
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