For the function $$f(x) = \begin{cases} x^2 - 4, & 0\le x < 4\\ 4, & x = 4\\ 3 x + 0, & 4 < x \end{cases}$$ use algebra to find each of the following limits:
$\lim\limits_{x\to 4^{+}}\, f(x) =$
$\lim\limits_{x\to 4^{-}}\, f(x) =$
$\lim\limits_{x\to 4}\, f(x) =$
(For each, enter DNE if the limit does not exist.)

Sketch a graph of $f(x)$ to confirm your answers.