#### Answer

Yes, see explanations.

#### Work Step by Step

If $f$ is an odd function of $x$, we have $f(-x)=-f(x)$ and $f$ is symmetric with respect to the origin.
Knowing $\lim_{x\to0^+}f(x)=3$, we have $\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(-x)=-\lim_{x\to0^+}f(x)=-3$
Thus, the answer is Yes.