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

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 + 8}{- 2 x^{2} - 7 x + 8} = \lim_{x \to -\infty}\frac{6 x + 4}{- 4 x - 7} = \lim_{x \to -\infty}\frac{6}{-4} = - \frac{3}{2}