Let I := [a, b] and let Un) be a sequence of functions on I -+ IRthat converges on I to
Chapter 8, Problem 11(choose chapter or problem)
Let I := [a, b] and let Un) be a sequence of functions on I -+ IRthat converges on I to I.Suppose that each derivative I~is continuous on I and that the sequence U~) is unifonnlyconvergentto g on I. Prove that I(x) - I(a) = f:g(t) dt and that I'(x) = g(x) for all x E I.
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