Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises - Page 70: 13

does not exist

$\lim\limits_{x \to 5}\frac{x^2-5x+6}{x-5}=\frac{(5)^2-5(5)+6}{(5)-5}=\frac{0}{0}=$indet so we have to do algebra $\lim\limits_{x \to 5}\frac{x^2-5x+6}{x-5}=\lim\limits_{x \to 5}\frac{(x-3)(x-2)}{(x-5)}$ We can't simplify or do anything further so the limit does not exist.