Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 1

$f(x)=\frac{x^{2}-36}{x-6}$ $f(6)=\frac{6^{2}-36}{6-6}=\frac{0}{0}$ The function has the indeterminate form $\frac{0}{0}$ at x=6. Transforming algebraically and canceling, we have $\frac{x^{2}-36}{x-6}=\frac{(x-6)(x+6)}{x-6}=x+6$ Evaluating using continuity, we get $\lim\limits_{x \to 6}\frac{x^{2}-36}{x-6}=\lim\limits_{x \to 6}(x+6)=6+6=12$

See the answer above.