## Calculus, 10th Edition (Anton)

$\lim\limits_{x \to 0^-} g(x) = \lim\limits_{x \to 0^+} g(x) = \lim\limits_{x \to 0} g(x) = g(0) = 4$
The function behaves very nicely around the point $x = 0$ (the function is continuous at $x = 0$) and thus, $\lim\limits_{x \to 0^-} g(x) = \lim\limits_{x \to 0^+} g(x) = \lim\limits_{x \to 0} g(x) = g(0) = 4$.