Question:
The Newton-Raphson iteration
$$
x_{n+1} = \frac{1}{3} \left( 2 x_n + \frac{N}{x_n^2} \right)
$$
is used to compute
The Newton-Raphson iteration
$$
x_{n+1} = \frac{1}{3} \left( 2 x_n + \frac{N}{x_n^2} \right)
$$
is used to compute
Show Hint
Newton-Raphson formula for cube root uses iteration with derivative \( 3x^2 \).
Updated On: May 28, 2025
- \( \sqrt[3]{N} \)
- \( \sqrt{N} \)
- \( \frac{1}{N} \)
- \( \frac{1}{\sqrt{N}} \)
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The Correct Option is A
Solution and Explanation
The iteration formula corresponds to the Newton-Raphson method for finding cube root of \( N \) by solving \[ x^3 - N = 0 \] Update formula: \[ x_{n+1} = x_n - \frac{x_n^3 - N}{3 x_n^2} = \frac{1}{3} \left( 2 x_n + \frac{N}{x_n^2} \right) \]
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