Suppose you want to compute the derivative of f(x) = sin(x) for any value of x0 using the first-order method, dh(x0). suppose your machine carries only 6 digits. considering only the effect of catastrophic subtraction, and allowing for the worst possible values of x0, within ±1 how many digits in dh(x0) would you trust for h = 10−n for n = 3 and n = 5?