Question

The iterative formula for finding \(2^{\frac{1}{5}}\) using Newton-Raphson method is

• A. \(\displaystyle x_{n+1}=\frac45x_n+\frac{2}{5x_n^4}\)
• B. \(\displaystyle x_{n+1}=\frac{5x_n^4}{x_n^5-2}\)
• C. \(\displaystyle x_{n+1}=x_n+\frac{x_n^5-2}{5x_n^4}\)
• D. \(\displaystyle x_{n+1}=x_n+\frac{5x_n^4}{x_n^5}\)

Hint:

For Newton-Raphson method, \[ \boxed{ x_{n+1} = x_n-\frac{f(x_n)}{f'(x_n)} } \] Choose \(f(x)\) such that its root is the required quantity.

Answer 1

The Correct Option is A