Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{x^{2} - 7 x + 5}{- 6 x^{2} + 2 x + 1}

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} - 7 x + 5}{- 6 x^{2} + 2 x + 1} = \lim_{x \to -\infty}\frac{2 x - 7}{2 - 12 x} = \lim_{x \to -\infty}\frac{2}{-12} = - \frac{1}{6}