Answer
$\lim\limits_{x \to a}p(x) = p(a)$
Work Step by Step
We can express $p(x)$ as follows:
$p(x) = b_n~x^n+b_{n-1}~x^{n-1}+...+b_1~x+b_0$
where each $b_i$ is a real number
We can find $\lim\limits_{x \to a}p(x)$:
$\lim\limits_{x \to a}p(x)$
$= \lim\limits_{x \to a}(b_n~x^n+b_{n-1}~x^{n-1}+...+b_1~x+b_0)$
$= \lim\limits_{x \to a}(b_n~x^n)+\lim\limits_{x \to a}(b_{n-1}~x^{n-1})+...+\lim\limits_{x \to a}(b_1~x)+\lim\limits_{x \to a}(b_0)$
$=b_n~a^n+b_{n-1}~a^{n-1}+...+b_1~a+b_0$
$= p(a)$
Thus, $\lim\limits_{x \to a}p(x) = p(a)$
