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

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{x^{2} - 7 x + 4}{- 4 x^{2} + 6 x - 4} = \lim_{x \to \infty}\frac{2 x - 7}{6 - 8 x} = \lim_{x \to \infty}\frac{2}{-8} = - \frac{1}{4}