1) $\lim_{x \to a} x = a$

2) $\lim_{x \to a} c = c$

3) $\lim_{x \to a} [cf(x)] = c\lim_{x \to a}f(x)$

4) $\lim_{x \to a} [f(x) \pm g(x)] = \lim_{x \to a}f(x) \pm \lim_{x \to a}g(x)$

5) $\lim_{x \to a} [f(x) g(x)] = \lim_{x \to a}f(x) \lim_{x \to a}g(x)$

6) $\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a}f(x)}{\lim_{x \to a}g(x)}$, only if $\lim_{x \to a}g(x) \neq0$

7) $\lim_{x \to a} [f(x)]^n=[\lim_{x \to a}f(x)]^n$

Where c is a constant, $\lim_{x \to a} f(x)$ and $\lim_{x \to a} g(x)$ exist.

Here is a fact that may be useful to you.

If $P(x)$ is a polynomial, then

$\lim_{x \to a} P(x)=P(a)$