Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{2 x^{2} + 24 x + 70}{9 x^{2} + 60 x - 21}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to -7}\frac{2 x^{2} + 24 x + 70}{9 x^{2} + 60 x - 21} = \lim_{x \to -7}\frac{4 x + 24}{18 x + 60} = \frac{4 (-7) + 24}{18 (-7) + 60} = \frac{2}{33}$