The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson's method is

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} + \frac{1}{3}\left( {{\text{N}} - {\text{x}}_{\text{k}}^3} \right)$$

$${{\text{x}}_{{\text{k}} + 1}} = \frac{1}{3}\left( {2{{\text{x}}_{\text{k}}} + \frac{{\text{N}}}{{{\text{x}}_{\text{k}}^2}}} \right)$$

$${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - \frac{1}{3}\left( {{\text{N}} - {\text{x}}_{\text{k}}^3} \right)$$

$${{\text{x}}_{{\text{k}} + 1}} = \frac{1}{3}\left( {2{{\text{x}}_{\text{k}}} - \frac{{\text{N}}}{{{\text{x}}_{\text{k}}^2}}} \right)$$

The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson's method is Correct Answer $${{\text{x}}_{{\text{k}} + 1}} = \frac{1}{3}\left( {2{{\text{x}}_{\text{k}}} + \frac{{\text{N}}}{{{\text{x}}_{\text{k}}^2}}} \right)$$

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Feb 20, 2025

Engineering Maths
Numerical Methods

The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson's method is

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