Step 1 - Initialization:

Start with an initial guess, let's call it x₀, for the root of the function f(x) = 0.

Step 2 - Iteration:

Use the formula:

x_n+1 = x_n - (f(x_n) / f'(x_n)

where:

• x_n+1 is the updated approximation of the root.
• x_n is the current approximation.
• f(x_n) is the value of the function at x_n.
• f'(x_n) is the derivative of the function at x_n.

Step 3 - Convergence Check:

Calculate the absolute error, ε, as:

ε = |x_n+1 - x_n|

If ε is smaller than a predefined tolerance or if a maximum number of iterations is reached, stop. Otherwise, go back to Step 2 with x_n+1 as the new approximation.

Step 4 - Output:

The final x_n+1 is an approximation of the root of the function (f(x) = 0).

The Newton-Raphson Method is a powerful tool for finding the roots of equations, but it may not always converge, and it requires knowledge of the derivative of the function.