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3 Answers

Best answer
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Answer is (c) 2.279 

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Shortcut to find an answer to such question in an exam.

Newton-Raphson method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It is one example of a root-finding algorithm.

Here f(x) = x3-3x-5

Just put the options one by one in f(x) and check whether we are getting "0.000..."(correct up to 3 decimal places) as the answer.

op A: x= 2.222   ie. f(x) = (2.222)3-3(2.222)-5 = -0.695354...  // op A is not correct

op B: x= 2.275   ie. f(x) = (2.275)3-3(2.275)-5 = -0.050453...  // op B is not correct

op C: x= 2.279   ie. f(x) = (2.279)3-3(2.279)-5 = -(0.000)236361...  // op C is correct root of given equation (upto 3 decimal places..

So Op C is the answer.

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c) by using this formula Xn+1 = Xn - (f(Xn) / f'(Xn))

Answer:

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