Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{2 x^{2} + 8 x - 9}{9 x^{2} - 2 x + 1}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to \infty}\frac{2 x^{2} + 8 x - 9}{9 x^{2} - 2 x + 1} = \lim_{x \to \infty}\frac{4 x + 8}{18 x - 2} = \lim_{x \to \infty}\frac{4}{18} = \frac{2}{9}