1. Consider a function f(x) = x² + x² 3 2 4x - 4. (a) Compute the minimum number of iterations required to find the root within the interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [-10, -1.5]. (c) State the exact roots of f(x) and construct two different fixed point functions g(x) such that f(x) = 0. (d) 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.
1. Consider a function f(x) = x² + x² 3 2 4x - 4. (a) Compute the minimum number of iterations required to find the root within the interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [-10, -1.5]. (c) State the exact roots of f(x) and construct two different fixed point functions g(x) such that f(x) = 0. (d) 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.
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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Need ans for part c and d only
![3
1. Consider a function f(x) = x³ + x² - 4x 4.
(a)
Compute the minimum number of iterations required to find the root within the
interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2.
(b)
Show 5 iterations using the Bisection Method to find the root of the above function
within the interval [-10, -1.5].
(c)
State the exact roots of f(x) and construct two different fixed point functions g(x)
such that f(x) = 0.
(d)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40b19d47-b91f-46d0-b325-24f63b3d8dff%2Ff2f0e05e-df7e-4353-9df8-a1a17635cc44%2F5890tqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
1. Consider a function f(x) = x³ + x² - 4x 4.
(a)
Compute the minimum number of iterations required to find the root within the
interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2.
(b)
Show 5 iterations using the Bisection Method to find the root of the above function
within the interval [-10, -1.5].
(c)
State the exact roots of f(x) and construct two different fixed point functions g(x)
such that f(x) = 0.
(d)
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.
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