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(Solution) - Let fn S Y be a sequence of C1 -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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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.

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