Consider a sequence of functions (fn)neN defined on [0, 1] by nx for x = [0,...

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Consider a sequence of functions (fn)neN defined on [0, 1] by nx for x = [0, 1]. 1+ n²r² (a) Show that (fn) is uniformly bounded on [0, 1] and evaluate du. fn(z) = Nx 1+n²x² [0,1] (b) Show that (fn) does not converge uniformly on [0, 1]. lim n-∞ Consider a sequence of functions (fn)neN defined on [0, 1] by nx for x = [0, 1]. 1+ n²r² (a) Show that (fn) is uniformly bounded on [0, 1] and evaluate du. fn(z) = Nx 1+n²x² [0,1] (b) Show that (fn) does not converge uniformly on [0, 1]. lim n-∞

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