Question: Let fn(x) := nx/(1 + nx) for x (0, 1). Show that (fn) converges non uniformly to an integrable function f and that 10

Let fn(x) := nx/(1 + nx) for x ∈ (0, 1). Show that (fn) converges non uniformly to an integrable function f and that ∫10 f(x)dx = lim ∫10 fn(x)dx.

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