Question

c) Obtain the cube root of 12 using Newton-Raphson formula.

Answer 1

Answer on Question #60833 – Math – Algorithms | Quantitative Methods

Question

c) Obtain the cube root of 12 using Newton-Raphson formula.

Solution

Newton-Raphson method is used to find zeros of the equation

$$f(x) = 0.$$

In this problem we set

$$f(x) = x^3 - 12, \quad f'(x) = 3x^2, \quad x_0 = 1;$$ $$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} = x_n - \frac{x_n^3 - 12}{3x_n^2} = \frac{2}{3}x_n + \frac{4}{x_n^2}.$$

So $\sqrt[3]{12} \approx 2.289428485107$.

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