1) [tex]\lim_{n \rightarrow +\infty}{\frac{\sqrt{2n^4-3n^2+1}}{1-5n-7n^2}}=\lim_{n \rightarrow +\infty}{\frac{\sqrt{2-\frac{3}{n^2}+\frac{1}{n^4}}}{\frac{1}{n^2}-\frac{5}{n}-7}}=\frac{-\sqrt{2}}{7}[/tex]
2) [tex]\lim_{n \rightarrow +\infty}{\frac{n^2+3n+1}{3-n}}=\lim_{n \rightarrow +\infty}{\frac{1+\frac{3}{n}+\frac{1}{n^2}}{\frac{3}{n^2}-\frac{1}{n}}}=+\infty[/tex]