Answered: (a) Use Newton's method to find x2 and…

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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part a continued... Give the function f(x) that you use for Newton's method and give the iterates x₂ and x₃ to 6 decimal places.

(b) Continue the process in part (a) further until the iterates converge to the solution. What is the solution and for which iterate is the solution first accurate to 6 decimal places?

(a) Use Newton's method to find x2 and x3, the second and third approximations to
the root of the equation 3 = 4+ sin x using x1 = 1.

Expert Solution

Step 1

To approximate the root of the equation

Consider a function

The formula for Newton's method is

Differentiating f(x) with respect to x,

Step 2

Given that first iteration, .

Thus, by Newton's formula

This is a second iteration up to 6 decimal places,

Now, for 3rd iteration by using newton's formula

This is the third iteration up to 6 decimal places.

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