Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{2 x^{2} + 12 x + 18}{x^{2} + 8 x + 15}$

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: $LaTeX: \lim_{x \to -3}\frac{2 x^{2} + 12 x + 18}{x^{2} + 8 x + 15} = \lim_{x \to -3}\frac{4 x + 12}{2 x + 8} = \frac{4 (-3) + 12}{2 (-3) + 8} = 0$