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I have this limit to evaluate $\lim\nolimits_{n \rightarrow +\infty} \int_{0}^{2} \arctan \left(\frac{1}{1+x^n}\right) dx.$

I have no idea how to solve this homework problem. Help!

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    Anytime you have a limit and a Lebesgue integral your mind should involuntarily think "this requires a $c$onvergence theorem!"2011-10-24

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HINT

$\arctan$ is bounded.