Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{8 x^{2} - 4 x - 8}{2 x^{2} + 5 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{8 x^{2} - 4 x - 8}{2 x^{2} + 5 x - 4} = \lim_{x \to -\infty}\frac{16 x - 4}{4 x + 5} = \lim_{x \to -\infty}\frac{16}{4} = 4