## Calculus: Early Transcendentals 8th Edition

let $r(x)=\frac{p(x)}{q(x)}$ where $p, q$ are polynomials $\lim\limits_{x \to a}r(x)=\lim\limits_{x \to a}\frac{p(x)}{q(x)}$ $=\frac{\lim\limits_{x \to a}p(x)}{\lim\limits_{x \to a}q(x)}$ $=\frac {p(a)}{q(a)}$ (using Exercise 57) $=r(a)$