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

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to -\infty}\frac{x^{2} + x + 6}{8 x^{2} - 6 x + 3} = \lim_{x \to -\infty}\frac{2 x + 1}{16 x - 6} = \lim_{x \to -\infty}\frac{2}{16} = \frac{1}{8}$