Limit Epsilon Delta Proof

[pinkgirl]

Hello! I am currently enrolled in an online calculus course, and I am stuck on this one problem:

Find the limit L. Then use the epsilon delta definition to prove that the limit is L.
lim ?x
x-->0
and I found that the limit of ?x as x approaches 0 is 0.
then I did:
|?x - 0| < ?
|?x | < ?

What should I do next? The text book didn't show me any examples of dealing with radicals...

 

[tkhunny]

Where's \(\displaystyle \delta\)?

 

[galactus]

\(\displaystyle \lim_{x\to 0}\sqrt[3]{x}=0\)

Given \(\displaystyle \epsilon> 0\)

\(\displaystyle \left|\sqrt[3]{x}-0\right|<\epsilon\)

\(\displaystyle \left|\sqrt[3]{x}\right|<\epsilon\)

\(\displaystyle \left|x\right|<{\epsilon}^{3}=\delta\)

Can you finish?. One more little step. What should we let delta be?.

 

[pinkgirl]

OH! so then I do:
0 < |x| < ? = ?^3
implying
[(|x|)^(1/3)] < [(?^3)^(1/3)] = ?

Is this how I am supposed to do it? To be honest, I am really confused about this whole Epsilon Delta Proof thing...I am sorry if I am doing anything stupid in this problem.