Question: Let fn(x) := nx/(1 + nx2) for x A := [0, ). Show that each fn is bounded on A, but the point wise

Let fn(x) := nx/(1 + nx2) for x ∈ A := [0, ∞). Show that each fn is bounded on A, but the point wise limit f of the sequence is not bounded on A. Does (fn) converge uniformly to f on A?

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