1) $\mathop {\lim }\limits_{n \to +\infty }(\sqrt[3]{n^3+n^2}-\sqrt{n^2-1})$
2) $\mathop {\lim }\limits_{n \to +\infty }(\sqrt{n^2+2n+3}+\sqrt[3]{n^2-n^3})$
3) $\mathop {\lim }\limits_{n \to +\infty }\frac{n-\sqrt{n^2+n\sqrt{n}}}{\sqrt{n+1}-\sqrt{n+2}}$
4) $\mathop {\lim }\limits_{n \to +\infty }\frac{1+3+5+...+(2n-1)}{n^2+1}$
5) $\mathop {\lim }\limits_{n \to +\infty }\frac{n\sqrt{1+2+3+...+2n}}{3n^2+n-2}$