//clc() //f(x) = exp(-x) - x //f'(x) = -exp(-x) - 1 //f"(x) = exp(-x) xr = 0.56714329; //E(ti+1) = -f"(x)* E(ti) / 2 * f'(x) Et0 = 0.56714329; Et1 = -exp(-xr)* ((Et0)^2) / (2 * (-exp(-xr) - 1)); disp("which is close to the true error of 0.06714329",Et1,"Et1 = ") Et1true = 0.06714329; Et2 = -exp(-xr)* ((Et1true)^2) / (2 * (-exp(-xr) - 1)); disp("which is close to the true error of 0.0008323",Et2,"Et2 = ") Et2true = 0.0008323; Et3 = -exp(-xr)* ((Et2true)^2) / (2 * (-exp(-xr) - 1)); disp("which is close to the true error",Et3,"Et3 = ") Et4 = -exp(-xr)* ((Et3)^2) / (2 * (-exp(-xr) - 1)); disp("which is close to the true error",Et4,"Et4 = ") disp("Thus it illustratres that the error of newton raphson method for this case is proportional(by a factor of 0.18095) to the square of the error of the previous iteration")