Find the limit as $n$ goes to infinity What would be the limit of $\cos(x/n)^{n^2}$ as $n\to\infty$ and how would you proceed with the proof?
I tried to use the exponential form of cosine: $$\frac{[e^{ix/n} + e^{-ix/n}]^{n^2}}{2^{n^2}}.$$
However, what is bothering me is that how I should get rid of the $n^2$ in the power. Please help. Thanks.

Hint : Take the logarithm, and apply l'Hopital.
