Suppose lim||P||0 S (P, f) = I E R. Show that if (Pn)neN is a sequence of partitions with ||Pn|| 0, then limn S (Pn, f) = I. Let f R[a, b]. i) If 0 on [a, b], show that f R[a, b]. ii) For n N, show that fn = R[a, b] where f'(x) = (f(x))". iii) If there is a 6 > 0 such that f(x) 6 for all x = [a, b], then 1/f = R[a, b]. A similar result holds if f(x) < -6 for all x = [a, b].