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Question Number 31708 by gunawan last updated on 13/Mar/18

$$\mathrm{Given}\mathrm{sequence}\mathrm{real}\mathrm{function}\left(f_n\right),$$$$f_n:[0,2]\to \mathbb{R},\mathrm{with}$$$$f_n\left(x\right)=\frac{x^n}{1+x^n}.n=1,2,3,...$$$$\mathrm{a}.\mathrm{Prove}\left(f_n\right)\mathrm{not}\mathrm{uniformly}\mathrm{convergent}\mathrm{on}[0,2]$$$$\mathrm{b}.\mathrm{Find}\underset{x\to \mathrm{\infty }}{\lim }{f}_n\left(x\right),x\in [0,2]$$

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