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
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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]
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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