5.5 Functions of Bounded Variation 4. Combine Lemma 4.28 and Theorem 3.39.

9. For the bounded case, prove that (L) J: 1f'(x)1 dx :S Var f :S (U) J: 1f'(x)1 dx.

5.6 Convex Functions 5. Use Remark 5.60.

8.

(b) See Exercise 7b.

(d) First prove that if ak ~ 0 and L:~oak diverges, then L:~oak = 00.
9.

(a) Is na2n :::; L:~n ak?
10. Use Corollary 6.9.