Answer
a) $\lim\limits_{x\to c^+}f(x)=0$
b) $\lim\limits_{x\to c^{-}}f(x)=0$
c) $\lim\limits_{x\to c}f(x)=0$
d) Continuous over the domain $(-\infty, 3)$and $(3, \infty)$ (in other words not continuous at $x=3.$)
Work Step by Step
a) As we approach c from the right, we get the limit to be equal to $0.$
b) As we approach c from the left, we get the limit to be equal to $0.$
c)The limit exists since $\lim\limits_{x\to c^+}f(x)=\lim\limits_{x\to c^{-}}f(x)$
d) The function is not continuous at $x=c$ since $f(c)\ne\lim\limits_{x\to c}f(x)$
