Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{5 x^{3} + 5 x^{2} - 3 x + 7}{- 4 x^{3} - 9 x^{2} + 8 x + 4}

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{5 x^{3} + 5 x^{2} - 3 x + 7}{- 4 x^{3} - 9 x^{2} + 8 x + 4} = \lim_{x \to -\infty}\frac{15 x^{2} + 10 x - 3}{- 12 x^{2} - 18 x + 8} = \lim_{x \to -\infty}\frac{10 \left(3 x + 1\right)}{- 6 \left(4 x + 3\right)} = \lim_{x \to -\infty}\frac{30}{-24} = - \frac{5}{4}