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Asked Nov 30, 2019
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Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.
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Exercise 4: [Hard] Use the Newton-Rhapson method to estimater to within four decimal places of accuracy.

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Expert Answer

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
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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

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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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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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