Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{2 x^{2} - 9 x - 4}{- 3 x^{2} + 4 x - 5}

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} - 9 x - 4}{- 3 x^{2} + 4 x - 5} = \lim_{x \to \infty}\frac{4 x - 9}{4 - 6 x} = \lim_{x \to \infty}\frac{4}{-6} = - \frac{2}{3}