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Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.

Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.

Advanced Engineering Mathematics
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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Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.
Transcribed Image Text:Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.
Expert Solution
Step 1
Construct a polynomial which has root as square root of 2 as follows. Let x T x- 0 Consider f(x)x-T Calculate the derivative of f(x)=x-r as f(x)=1 wwww f(x,) (x,) Note that, the Newton Raphson method is given by Start with x 3 as follows Now, compute the value of x using Newton Raphson method as follows. f(xc 3-7 -3 1 =T
Step 2
Now, compute the value of x, using Newton Raphson method as follows f(x) f'(x,) л — п 1 From the above two steps, it can be concluded that x3 will not work. xg 3.5 as follows Now start with initial solution Now, compute the value of x using Newton Raphson method as follows f(x,) f(%) 3 = 3.5 1 = 3.1416
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