Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{4 x^{3} - 8 x^{2} + 5 x + 4}{4 x^{3} - 8 x^{2} - 4 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{4 x^{3} - 8 x^{2} + 5 x + 4}{4 x^{3} - 8 x^{2} - 4 x - 4} = \lim_{x \to -\infty}\frac{12 x^{2} - 16 x + 5}{12 x^{2} - 16 x - 4} = \lim_{x \to -\infty}\frac{8 \left(3 x - 2\right)}{8 \left(3 x - 2\right)} = \lim_{x \to -\infty}\frac{24}{24} = 1