1. $lim \frac{cos2n}{n^{2}-n+1}$
2. $lim\left ( \frac{1}{n\sqrt{n}+1}+\frac{1}{n\sqrt{n}+2}+...+\frac{1}{n\sqrt{n}+n} \right )$
3. $lim \left ( \sqrt{n^{2}-1}-n \right )$
4. $lim \left ( \sqrt{n^{2}+n}-\sqrt{n^{2}+1} \right )$
5. $lim \sqrt{n-1}\left ( \sqrt{n+2}-\sqrt{n} \right )$
