Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{4 x^{2} - 2 x + 4}{5 x^{2} - 9 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{4 x^{2} - 2 x + 4}{5 x^{2} - 9 x + 6} = \lim_{x \to -\infty}\frac{8 x - 2}{10 x - 9} = \lim_{x \to -\infty}\frac{8}{10} = \frac{4}{5}