Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{8 x^{2} + 6 x + 9}{5 x^{2} - 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{8 x^{2} + 6 x + 9}{5 x^{2} - x + 6} = \lim_{x \to -\infty}\frac{16 x + 6}{10 x - 1} = \lim_{x \to -\infty}\frac{16}{10} = \frac{8}{5}