Let E := {c1, c2, . . .} and let F be continuous on [a, b] and Fʹ(x) = f(x) for x [a, b]E and

Let E := {c1, c2, . . .} and let F be continuous on [a, b] and Fʹ(x) = f(x) for x ˆˆ [a, b]E and f(ck) := 0. We want to show that f ˆˆ R*[a, b] and that equation (5) holds.
(a) Given ε > 0 and t ˆˆ [a, b]E, let δε(t) be defined as in the proof of 10.1.9. Choose δε(ck) > > 0 such that if |z - ck|

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