Question: ............. (4) Consider the sequence of functions (fn) defined by fn(x) = nx 1+nx for x 2 0. (a) Find the pointwise limit f(x) =

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(4) Consider the sequence of functions (fn) defined by fn(x) = nx 1+nx for x 2 0. (a) Find the pointwise limit f(x) = limn > fn(x) for x 2 0. (b) Let a > 0. Prove or disprove: (fn) converges uniformly to f on [a, co) . (c) Prove or disprove: (fn) converges uniformly to f on [0, co)

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