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Question

The Newton-Raphson method formula for finding the square root of a real number N from the equation x2−N=0 is

A
xi+1=5xi2
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B
xi+1=3xi2
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C
xi+1=12(xi+Nx2i)
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D
xi+1=12(xi+Nxi)
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Solution

The correct option is D xi+1=12(xi+Nxi)
xi+1=xif(xi)f(xi)
f(x)=x2N
f(x)=2x
xi+1=xix2iN2xi=xixi2+N2xi
=xi2+N2xi=12(xi+Nxi)

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