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Let $f_{n}\left( x\right) =\dfrac {x^{n}} {1+x^{n}},x\in \left[ 0,2\right]$

Does $f_{n}$ converge uniformly?

I know that $f_{n}$ converges pointwise to $0$ for $x\in \left[ 0,1\right)$, $1/2$ for $x=1$, and $1$ for $x\in \left(1,2\right]$, but I need help showing if it converges uniformly or not. Thanks!

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Never mind, I figured it out! –  user53527 Dec 18 '12 at 5:06
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1 Answer

Hint: If a sequence of continuous functions converges uniformly, then it converges to a continuous function.

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