Answer
$ a.\quad+\infty$
$ b.\quad-\infty$
Work Step by Step
$a.$
When $x\rightarrow 0^{+}$, the numerator is positive, and $x^{1/3} $ (the cube root of x) also approaches 0 from the positive side, so the denominator approaches 0 from the positive side, so the whole fraction $\displaystyle \frac{2}{3x^{1/3}}\rightarrow+\infty \qquad$ ... ( $\displaystyle \frac{pos.}{pos.}$ )
$b.$
When $x\rightarrow 0^{-}$, the numerator is positive, and $x^{1/3} $ (the cube root of x) also approaches 0 from the negative side, so the denominator approaches 0 from the negative side, so the whole fraction $\displaystyle \frac{2}{3x^{1/3}}\rightarrow-\infty \qquad$ ... ( $\displaystyle \frac{pos.}{neg.}$ )
