Suppose that and are of bounded variation on a closed interval [a, b). a) Prove

Suppose that ϕ and ψ are of bounded variation on a closed interval [a, b).
a) Prove that αϕ is of bounded variation on [a, b] for every a ˆˆ R.
b) Prove that ϕψ is of bounded variation on [a, b].
c) If there is an ε0 > 0 such that

prove that 1/Ï• is of bounded variation on [a, b].

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φ(x) eo, x E [a, b].