With exact rounding, we know that each elementary operation has a relative error which is bounded in terms of the rounding unit n; e.g., for two foating point numbers x and y, (x + y) = (x + y)(1 + E); |E| <= n. But does a similar result hold for elementary functions such as sin, ln and exponentiation? In other words is it true that for a function f(x), (f(x)) = f(x)(1+CE), for some (hopefully small) positive constant C? Note: E=epsilon a) Consider f(x) = x2. Compute the a formula for the relative error in f(x) assuming the relative error in x is e and ignoring error in evaluating f(x). Does (f(x)) = f(x)(1 + CE) hold for this example? b) Repeat question a but now for f(x) = ex. c) Show that if (f(x)) = f(x)(1 + CE) holds, then f(x) must have the form f(x) = axb with constants a and b.