University of California, Berkeley

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

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

You must be logged in to like a video.

You must be logged in to bookmark a video.

## 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

## Recommended Questions