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## Let fn: R –> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges uniformly on R to a function f. b) Show that f'(x) = limn –>infinity f’n(x), For all x does not = 0, but this equality is false for x = 0. c)What assumption in the theorem on the interchange of the limit and the derivative is missing? I am stuck with that last part (C).

Let fn: R –> R be defined by : fn(x)= x/(1+nx2), For all n >= 1.

a) Show that {fn} converges uniformly on R to a function f.

b) Show that f'(x) = limn –>infinity f’n(x), For all x does not = 0, but this equality is false for x = 0.

c)What assumption in the theorem on the interchange of the limit and the
derivative is missing?

I am stuck with that last part (C).

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