Question: Let fn: S Y be a sequence of C1 functions on an open set S, and define Suppose that the sequence of derivatives Dfn converges

Let fn: S †’ Y be a sequence of C1 functions on an open set S, and define

Let fn: S †’ Y be a sequence of C1

Suppose that the sequence of derivatives Dfn converges uniformly to a function g: S †’ BL(X, Y). Then f is differentiable with derivative Df = g.

f(x) = lim fn(x)

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