Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{8 x^{3} - 5 x^{2} + 7 x + 1}{8 x^{3} - 6 x^{2} - 7 x - 9}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 3 times gives: LaTeX: \lim_{x \to -\infty}\frac{8 x^{3} - 5 x^{2} + 7 x + 1}{8 x^{3} - 6 x^{2} - 7 x - 9} = \lim_{x \to -\infty}\frac{24 x^{2} - 10 x + 7}{24 x^{2} - 12 x - 7} = \lim_{x \to -\infty}\frac{2 \left(24 x - 5\right)}{12 \left(4 x - 1\right)} = \lim_{x \to -\infty}\frac{48}{48} = 1