Q1. Subtractive cancellation occurs when two nearly equal numbers are subtracted. This is a common cause of noticeable round-off error. Let's see how this affects numerical differentiation. a) Write a code to approximate the first derivative of f = e* at x = 0 using the forward difference formula (exth - e*)/h with h = 10-, 10-, 10-,..., 10-10. Tabulate the results and true errors. Plot true error vs. h. Comment on the drop rate of the error. b) Repeat part (a) using the central difference formula (exth ex-h)/(2h).