Answer
(a) $\lim_{x\to0^+}f(x)$ does not exist.
(b) $\lim_{x\to0^-}f(x)=0$
(c) $\lim_{x\to0}f(x)$ does not exist.
Work Step by Step
(a) $\lim_{x\to0^+}f(x)$ does not exist since as $x$ approaches $0$ from the right, $f(x)$ fluctuates continuously from $-1$ to $1$ and vice versa. Therefore, it does not approach any single stable value, $\lim_{x\to0^+}f(x)$, hence, does not exist.
(b) $\lim_{x\to0^-}f(x)=0$. As $x$ approaches $0$ from the left, $f(x)$ gets arbitrarily close to $0$.
(c) Since $\lim_{x\to0^+}f(x)$ does not exist, $\lim_{x\to0}f(x)$ cannot exist.
