Answer
a) $\lim\limits_{x \to 0^-}$f(x)=1
b) $\lim\limits_{x \to 0^+}$f(x)=0
c) $\lim\limits_{x \to 0}$f(x) does not exist because $\lim\limits_{x \to 0^-}$f(x) $\ne$ $\lim\limits_{x \to 0^+}$f(x)=0
Work Step by Step
a) as x approaches 0 from the left-hand side, f(x) moves towards 1
b) as x approaches 0 from the right-hand side, f(x) moves towards 0
c) The limit does not exist because as x approaches 0 from both sides, for f(x) from the right side ≠ f(x) from the left side.
