Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 7 x^{2} + 3 x - 2}{4 x^{2} - 3 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{- 7 x^{2} + 3 x - 2}{4 x^{2} - 3 x - 6} = \lim_{x \to -\infty}\frac{3 - 14 x}{8 x - 3} = \lim_{x \to -\infty}\frac{-14}{8} = - \frac{7}{4}