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

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 + 3}{- 8 x^{2} + 9 x + 6} = \lim_{x \to -\infty}\frac{4 x + 9}{9 - 16 x} = \lim_{x \to -\infty}\frac{4}{-16} = - \frac{1}{4}