5. Suppose we want to find the root of the function f(x) = x³ + 3x - 5. (a) How can we verify that the function has a root in [1,2]? (b) Use the false position method to find the root. Show the computations for the first 3 iterations. Compute the approximate relative error in each iteration. (c) Using 1 as an initial guess, use the secant method to find the root of the function. Show the computations of first 4 iterations. What is the approximate relative error in each iteration. [The answer should be close to 1.1541]
5. Suppose we want to find the root of the function f(x) = x³ + 3x - 5. (a) How can we verify that the function has a root in [1,2]? (b) Use the false position method to find the root. Show the computations for the first 3 iterations. Compute the approximate relative error in each iteration. (c) Using 1 as an initial guess, use the secant method to find the root of the function. Show the computations of first 4 iterations. What is the approximate relative error in each iteration. [The answer should be close to 1.1541]
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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![5. Suppose we want to find the root of the function f(x) = x³ + 3x - 5.
(a) How can we verify that the function has a root in [1,2]?
(b) Use the false position method to find the root. Show the computations for the first 3
iterations. Compute the approximate relative error in each iteration.
(c) Using 1 as an initial guess, use the secant method to find the root of the function. Show the
computations of first 4 iterations. What is the approximate relative error in each iteration.
[The answer should be close to 1.1541]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a172bd2-0a97-4dc8-8c4f-1532515d0b37%2F720f9959-d71f-4347-8b32-31f872e04012%2F0w9zya_processed.png&w=3840&q=75)
Transcribed Image Text:5. Suppose we want to find the root of the function f(x) = x³ + 3x - 5.
(a) How can we verify that the function has a root in [1,2]?
(b) Use the false position method to find the root. Show the computations for the first 3
iterations. Compute the approximate relative error in each iteration.
(c) Using 1 as an initial guess, use the secant method to find the root of the function. Show the
computations of first 4 iterations. What is the approximate relative error in each iteration.
[The answer should be close to 1.1541]
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