Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 1}\frac{4 x^{2} - 12 x + 8}{4 x^{2} - 12 x + 8}$

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: $LaTeX: \lim_{x \to 1}\frac{4 x^{2} - 12 x + 8}{4 x^{2} - 12 x + 8} = \lim_{x \to 1}\frac{8 x - 12}{8 x - 12} = \frac{8 (1) - 12}{8 (1) - 12} = 1$