Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 3 x^{2} + 4 x - 1}{8 x^{2} + 6 x - 2}

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