Proving polynomial limit theorems I am pretty confused on this math question. It is a two-parter but I'm not sure what part a is asking me, perhaps someone on StackExchange could help.
The question reads as follows:
(a) If p is a polynomial, prove, using limit theorems, that
$$\lim_{x\to a}p\left(x\right) = p\left(a\right)$$
(b) Use the result in (a) to evaluate
$$\lim_{x\to 0^-}\left(x^3 – 8x^2 + 2x – 1\right)$$
Could somebody give me some hints about 'proving' part a with limit theorems? I was under the impression that it was a limit theorem. Because I have a polynomial wouldn't I just replace the value of $x$ with $a$? What else can I say about it? And wouldn't I just replace $x$ with $0$ in part b?

Since any polynomial $p$ is continuous on $\Bbb R$ then we have
$$\lim_{x\to a}p(x)=p(a)$$
so to find the limit just evaluate the polynomial on $a$.
