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University of California, Berkeley

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Problem 51

Using the $\varepsilon$ -\delta Definition of Limit In Exercises $45-56$ , find the limit $L$ . Then use the $\varepsilon-\delta$ definition to prove that the limit is $L$ .

$$\lim _{x \rightarrow 0} \sqrt[3]{x}$$

Answer

$L=0,$ see explanation for proof

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## Discussion

## Video Transcript

Okay, We have the limit. The next thing you know, that was scary. Braddock. You good, in fact, which is equal to what? You know, we just get don't. So whenever are for that's longer. Do you think so? There's a delta. Get it up. What's that? Whenever our function the cube back minus Ireland, they've left the next one. We have that X minus delta. So this is equal to after You'd always like you, but and we say this is an excellent but we know that for this is equal to nothing. So basically, what we do is you can set delta equal to That's a long queue so we could have their own Weston next money Still lesson Kelso, which is excellent. You and that implied that. Thank you, Groot. Or you had a few boot back myself. You could too. Thank you, Brit. Which is equal to the cube root of absolutely back. We should have to tell you left and and we said Delta is equal to after long cute. Who is this kid? The one the reset satisfied the condition that after that dressed