Newton raphson method

The formula for the Newton-Raphson method is:

$$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$$

where:

• $x_{n+1}$ is the next approximation of the root.
• $x_n$ is the current approximation of the root.
• $f(x_n)$ is the value of the function at $x_n$.
• $f'(x_n)$ is the value of the derivative of the function at $x_n$.

To use this method, you need:

1. A function $f(x)$ for which you want to find a root.
2. The derivative of the function, $f'(x)$.
3. An initial guess, $x_0$, that is reasonably close to the actual root.

The process involves repeatedly applying the formula to get closer and closer to the root. The iteration stops when the difference between successive approximations is below a certain tolerance, or when $f(x_n)$ is sufficiently close to zero.