Limit of a function

Keywords: liimit of a function, properties

If both functions have finite limits, then

$\underset{x\to {x}_{0}}{lim}\left[f\left(x\right)±g\left(x\right)\right]=\underset{x\to {x}_{0}}{lim}f\left(x\right)±\underset{x\to {x}_{0}}{lim}g\left(x\right)$
$\underset{x\to {x}_{0}}{lim}\left[f\left(x\right)·g\left(x\right)\right]=\underset{x\to {x}_{0}}{lim}f\left(x\right)·\underset{x\to {x}_{0}}{lim}g\left(x\right)$