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].
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].
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 a and b
![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%2F10ca7af6-301d-4aff-930b-c45b8a811dc9%2Fm3f2d4v_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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