A) \[3/2\]
B) \[7/4\]
C) \[97/56\]
D) \[347/200\]
Correct Answer: C
Solution :
Key Idea: The Newton-Raphson formula for the function\[f(x)\]is \[{{x}_{n+1}}={{x}_{n}}-\frac{f({{x}_{n}})}{f'({{x}_{n}})}\] Let \[f(x)={{x}^{2}}-3\] On differentiating w.r.t. x, we get \[f'(x)={{x}^{2}}-3\] \[\therefore \]By using Newton-Raphson of first iteration. \[{{x}_{1}}={{x}_{0}}-\frac{f({{x}_{0}})}{f'({{x}_{0}})}\] \[=\frac{3}{2}-\frac{\frac{9}{4}-3}{2\times \frac{3}{2}}=\frac{3}{2}+\frac{1}{4}=\frac{7}{4}\] Second iteration is \[{{x}_{2}}={{x}_{1}}-\frac{f({{x}_{1}})}{f'({{x}_{1}})}\] \[=\frac{7}{4}-\frac{\frac{1}{16}}{\frac{7}{2}}=\frac{7}{4}-\frac{1}{56}\] \[=\frac{97}{56}\].
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