Bisection method

To make up the newton's method. Consider function f(x) = x^2 - 5. we are seeking the root. f(x + dx) = f(x) + f'(x) dx x_new = x + dx

taylor expansion sqrt(5) = sqrt(4 + 1) first order: sqrt(5) ~= 2 + 1/4 = 2.25 second order: sqrt(5) ~= 2 + 1/4 - 1/64 = 2.2344 third order: sqrt(5) ~= 2 + 1/4 - 1/64 + 1/512 = 2.2363 ...