(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, x, = 0. Consider up to five decimal places. [Error bound is 1 x 10^-3] [Must use Radian Mode of calculator]

(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, x, = 0. Consider up to five decimal places. [Error bound is 1 x 10^-3] [Must use Radian Mode of calculator]

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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Question

Need ans for part b 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]

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