# How do you prove the statement lim as x approaches 0 for x^3=0 using the epsilon and delta definition?

Oct 7, 2015

Use the fact that if $\left\mid x \right\mid < 1$, then $\left\mid {x}^{3} \right\mid < \left\mid x \right\mid$.

#### Explanation:

Given $\epsilon > 0$, choose $\delta = \min \left\{1 , \epsilon\right\}$

Now if $0 < \left\mid x - 0 \right\mid < \delta$ then . . .

etc. to show

$\left\mid {x}^{3} - 0 \right\mid < \epsilon$.