(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.
(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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 50E
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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?
Transcribed Image Text:(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
a)
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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