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