Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -\infty}\frac{4 x^{2} - x + 8}{6 x^{2} + 8 x - 4}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to -\infty}\frac{4 x^{2} - x + 8}{6 x^{2} + 8 x - 4} = \lim_{x \to -\infty}\frac{8 x - 1}{12 x + 8} = \lim_{x \to -\infty}\frac{8}{12} = \frac{2}{3}$