$\lim\limits_{n\to\infty}\int^{2}_0 x^4 \cos(x/n)$ $$\lim\limits_{n\to\infty}\int^{2\pi}_0 x^4 \cos(x/n)$$

This is my solution for the problem. I cannot upload the rest of the solution, but all I did after that was making more calculation and got to the fact that the limit is 0, but my teacher told me it is not.Could you help me?

I also did the calculus and I think that you forgot to multiplicate the final result of the integral with $n^5$ and th result would be 32/5. Also, I did the same mistake when I solved your problem.
Also, https://www.wolframalpha.com/input/?i=%5Clim+integral_0%5E2+x%5E4+%5Ccos+%5Cfrac%7Bx%7D%7Bn%7D+dx+n-%3Einf
