GATE CS 2014 Set 2 — Question 56
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Engineering Mathematics → Calculus → Differentiation
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Question
In the Newton-Raphson method, an initial guess of is made and the sequence is obtained for the functionConsider the statements
(I) .
(II) The method converges to a solution in a finite number of iterations.Which of the following is TRUE?
(I) .
(II) The method converges to a solution in a finite number of iterations.Which of the following is TRUE?
Correct answer
(A) Only I
Solution
Given function:
Derivative: Newton-Raphson formula: Iteration 1:
Iteration 2:
Iteration 3:
Since , the sequence will oscillate:
Thus, .Statement (I) is TRUE because .
Statement (II) is FALSE because the sequence oscillates between 0 and 2 and does not converge.Therefore, Only I is true.
Derivative: Newton-Raphson formula: Iteration 1:
Iteration 2:
Iteration 3:
Since , the sequence will oscillate:
Thus, .Statement (I) is TRUE because .
Statement (II) is FALSE because the sequence oscillates between 0 and 2 and does not converge.Therefore, Only I is true.
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