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GATE | GATE CS 2010 | Question 2

Last Updated : 14 Feb, 2018
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Newton-Raphson method is used to compute a root of the equation x2-13=0 with 3.5 as the initial value. The approximation after one iteration is
 

(A)

3.607
 

(B)

3.667
 

(C)

3.676
 

(D)

3.575
 



Answer: (A)

Explanation:

In Newton-Raphson\’s method, We use the following formula to get the next value of f(x). f\'(x) is derivative of f(x). 
x_{n+1} = x_{n}- \\frac{f(x_{n})}{f\'(x_{n})}

 

f(x)  =  x2-13
f\'(x) =  2x

Applying the above formula, we get
Next x = 3.5 - (3.5*3.5 - 13)/2*3.5
Next x = 3.607


 



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