Saturday, 22 July 2017

Computing the limit of ncdotarccosleft(left(fracn21n2+1right)cos(1/n)right)

I need to solve this earth's wonder:




lim





I have tried to write down it using e^{v \ln u},and then used L'Hôpital's rule, but with no luck, i'm constantly getting indeterminate form like \infty-\infty inside \ln which makes another application of L'Hôpital impossible.



My professor told me (with great smile on its face) that if i use Taylor expansion, it will lead me into the abyss...



any hints about possible rewriting this limit and what i should use would be VERY helpful. Thanks in advance.

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