Question: Let fn (x) := xn/n for x [0, 1]. Show that the sequence (fn) of differentiable functions converges uniformly to a differentiable function f

Let fn (x) := xn/n for x ∈ [0, 1]. Show that the sequence (fn) of differentiable functions converges uniformly to a differentiable function f on [0, 1], and that the sequence (fʹn) converges on [0, 1] to a function g, but that g(1) ≠ fʹ(1).

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