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

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{9 x^{2} + 3 x + 2}{3 x^{2} + 5 x - 9} = \lim_{x \to -\infty}\frac{18 x + 3}{6 x + 5} = \lim_{x \to -\infty}\frac{18}{6} = 3