Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{2 x^{2} - 3 x - 7}{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{2 x^{2} - 3 x - 7}{x^{2} - 9 x - 6} = \lim_{x \to -\infty}\frac{4 x - 3}{2 x - 9} = \lim_{x \to -\infty}\frac{4}{2} = 2