Newton's method

Iteration Process: 1. Start with an initial guess x₀ 2. Draw the tangent line to the function at point (x₀, f(x₀)) 3. Find where this tangent crosses the x-axis → new approximation x₁ 4. Repeat until desired accuracy is achieved

Mathematical Formula: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)

Where: - xₙ is the current approximation - f(xₙ) is the function value at xₙ - f'(xₙ) is the derivative at xₙ

Implementation calculating the square root

#define ABS(x) ((x)>0?(x):(-x))

double f(double x, double guess, double eps){
    double newguess = (guess+x/guess)/2;
    if(ABS(guess * guess - x) < eps){
        return guess;
    }else{
        return f(x,newguess,eps);
    }
}