Answer
please see step-by-step
Work Step by Step
In exercise 57, we found that for a polynomial $p(x)$,
$\displaystyle \lim_{x\rightarrow a}p(x)=p(a) \qquad (*)$
r is a rational function, $r(x)=\displaystyle \frac{p(x)}{q(x)}$
$p(x)$ and $q(x)$ are polynomials. Also, suppose that $q(a)\neq 0$.
$\displaystyle \lim_{x\rightarrow a}r(x)=\lim_{x\rightarrow a}\frac{p(x)}{q(x)}$=
... Law 5, The limit of a quotient...
$=\displaystyle \frac{\lim_{x\rightarrow a}p(x)}{\lim_{x\rightarrow a}q(x)}$
... by the result of Exercise 57, (*)
$=\displaystyle \frac{p(a)}{q(a)}$
$=r(a)$
so, $\displaystyle \lim_{x\rightarrow a}r(x)=r(a)$
