Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{8 x^{2} + 9 x - 9}{3 x^{2} - 6 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{8 x^{2} + 9 x - 9}{3 x^{2} - 6 x - 1} = \lim_{x \to \infty}\frac{16 x + 9}{6 x - 6} = \lim_{x \to \infty}\frac{16}{6} = \frac{8}{3}