GATE | GATE CS 2010 | Question 2

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) 3.575
(B) 3.676
(C) 3.667
(D) 3.607

Answer: (D)

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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