Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -\infty}\frac{5 x^{2} - 8 x + 7}{5 x^{2} + 8 x + 2}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to -\infty}\frac{5 x^{2} - 8 x + 7}{5 x^{2} + 8 x + 2} = \lim_{x \to -\infty}\frac{10 x - 8}{10 x + 8} = \lim_{x \to -\infty}\frac{10}{10} = 1$