[!J. This exercise is used in Section e14.3. Suppose that ¢ and 'lj; are of bounded variation on a closed interval [a, b].

(a) Prove that ex¢ is of bounded variation on [a, b] for every ex E R.

(b) Prove that ¢'lj; is of bounded variation on [a, b].

(c) If there is an co > 0 such that

¢(x) ~ co, x E [a, b], prove that 1/¢ is of bounded variation on [a, b].