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