Here is a (non-exhaustive) list of the limit laws.
Basic laws
lim where c is a constant
\lim\limits_{x\to a} x = a
Addition law
\lim\limits_{x\to a} (f(x) + g(x)) = \lim\limits_{x\to a} f(x) + \lim\limits_{x\to a} g(x)
Provided \lim\limits_{x\to a} f(x) and \lim\limits_{x\to a} g(x) exist.
Subtraction law
$\lim\limits_{x\to a} (f(x)...