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)

3.607

(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). 

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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