Problem

Find the limit. Use l'Hospital's Rule where appro…

01:49

Problem 32 Medium Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to \infty} \frac{(\ln x)^2}{x} $

Name: find the limit use lhospitals rule where appropriate if there is a more elementary method conside 25
Uploaded: 2018-02-05
Duration: 2 min 22 s
Channel: Numerade
Description: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why. $ \displaystyle \lim_{x\to \infty} \frac{(\ln x)^2}{x} $

Answer

$\lim _{x \rightarrow \infty} \frac{\ln (x)^{2}}{x}=0$

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Watch More Solved Questions in Chapter 4

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 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Video Transcript

Yeah, Okay, fine. That the limit us locked us rule there a proper great if they're some are elementary. My third Consider using it. Okay, here is the limit as X goes to infinity. So if you're plucking infinity to the cop log rhythm functional algorithm infinity, which is infinity. So you square it, Takis infinity. And he wanted by another run that another x x goes to infinity. So there's this infinite he divided by infinity, which is saying determined the phone so we can use the locked house rule to write it as the limit as the axe goes to infinity that you're a tip off that hop because two times Lok X, use the power rule force first and then use the train rule to find a curative off his side function that isthe one over X. And then he wanted by the curative off the denominator that hiss one. So, actually you just need to find the limit off this function and that his Seiko too. Since the limit has the linear property, you can put a truly in front that Islamic as X goes to infinity now algorithm function of X times where our ex that means this one divided by X. Okay, So here you feel plaque in infinity to here and here. That is also infinite. He divided by infinity, which is? They come in the form so you can use the love house rule again. Practice as the limit. A few times the limit has goes to infinity that the early if off the top fishes where our ex divided by the curative off the denominator like this one. So you get the limit as axe ghost waiting for that hero our acts that his zero so two times zero is zero.

Mengsha Y.