(c) Given two sequences (fn)neN, (In)nEN C C[0, 1] of continuous functions on the closed unit interval [0, 1] defined by nx nx fn(2) = and g(x) = 1 + nx² 1+ n²x² Find the limit f and g, respectively of each sequence, if it exists. Which of these sequences converge uniformly on [0, 1]? That is, do f and g belong to C[0, 1] or not? "

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