This is the engine room of the Numerical Methods topic. You will often be given an equation that cannot be rearranged for $x$, forcing you to create an iterative formula $x_n+1 = g(x_n)$.
(Answers: Root ≈ 0.44285; quadratic convergence because f’(root) ≠ 0; bisection slower because linear convergence.) numerical methods madasmaths
"The equation ( e^x - 3x = 0 ) has a root in ( [0, 0.5] ). Perform one bisection iteration. What is the maximum possible error in your approximation after this iteration?" This is the engine room of the Numerical Methods topic
, including cobweb and staircase diagrams to visualize convergence. Newton-Raphson Method: quadratic convergence because f’(root) ≠ 0