Answer
$\lim\limits_{x \to 0}$$\sqrt[3] x$ = 0 for given epsilon > 0, we choose delta =$(epsilon)^{3}$
Work Step by Step
From only one side values are approaching to the limit so, by definition we can not take the limit but since the domain of function is [0,$\infty$) and it is obvious that 0 is the limit point, So , we can say $\lim\limits_{x \to 0}$$\sqrt[3] x$ = 0.
proof using epsilon and delta: |$\sqrt[3] x$| < epsilon whenever |x - 0| < delta so for given epsilon > 0, we choose delta =$(epsilon)^{3}$
