1. Consider A function f(x) = x³ - 7x² + 4x + 12. (a) (b) (c) (d) (e) Construct two different fixed point functions g(x) such that f(x) = 0. Compute the convergence rate of each fixed point function g(x) obtained in the previous part, and state which root it is converging to or diverging. How many iterations will be required to find the root if the machine epsilon is 1.4 × 10-18. Show 4 iterations using the Bisection Method to find the root of the above function within the interval [4.25, 8.95]. Starting from xo = 2.26 find the approximate root of f(x) up to four iterations by applying Aitken acceleration appropriately. Express your result up to five decimal places.
1. Consider A function f(x) = x³ - 7x² + 4x + 12. (a) (b) (c) (d) (e) Construct two different fixed point functions g(x) such that f(x) = 0. Compute the convergence rate of each fixed point function g(x) obtained in the previous part, and state which root it is converging to or diverging. How many iterations will be required to find the root if the machine epsilon is 1.4 × 10-18. Show 4 iterations using the Bisection Method to find the root of the above function within the interval [4.25, 8.95]. Starting from xo = 2.26 find the approximate root of f(x) up to four iterations by applying Aitken acceleration appropriately. Express your result up to five decimal places.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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