Answer
a) $\lim\limits_{x\to c^+}f(x)=0$
b) $\lim\limits_{x\to c^{-}}f(x)=2$
c) $\lim\limits_{x\to c}f(x)$ does not exist.
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 $2.$
c)The limit does not exist since $\lim\limits_{x\to c^+}f(x)\ne\lim\limits_{x\to c^{-}}f(x).$
d) The function is not continuous at $x=c$ since $\lim\limits_{x\to c}f(x)$ does not exist.
