2 3. (a) Consider the function f(x) = x - x + 1 and starting point x₁ = 0. Show that the sequence using Newton's method x1, x2, fails to approach a root of f(x).
2 3. (a) Consider the function f(x) = x - x + 1 and starting point x₁ = 0. Show that the sequence using Newton's method x1, x2, fails to approach a root of f(x).
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 only
![3. (a)
Consider the function f(x) =
sequence using Newton's method x1, x2,
2
x - x + 1 and starting point x₁ = 0. Show that the
fails to approach a root of f(x).
(b)
Consider the function f(x) = cos(2x) - sin(x). Compute the root of the function
using Newton's method with Aitken's acceleration and starting point, x₁ = 0. Consider up to five
decimal places. [Error bound is 1 x 10^-3] [Must use Radian Mode of calculator]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40b19d47-b91f-46d0-b325-24f63b3d8dff%2Ff84f6294-c07a-487e-9409-540d797d9cf9%2Fq5uj9lf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. (a)
Consider the function f(x) =
sequence using Newton's method x1, x2,
2
x - x + 1 and starting point x₁ = 0. Show that the
fails to approach a root of f(x).
(b)
Consider the function f(x) = cos(2x) - sin(x). Compute the root of the function
using Newton's method with Aitken's acceleration and starting point, x₁ = 0. Consider up to five
decimal places. [Error bound is 1 x 10^-3] [Must use Radian Mode of calculator]
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