Problem

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

01:31

Problem 58 Hard 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 0^+} (\tan 2x)^x $

Answer

1

More Answers

04:18

Wen Z.

01:30

Amrita B.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

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

Anna Marie V.

Campbell University

Heather Z.

Oregon 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

So here the function that we're given is the limit. As X approaches zero from the right of the tangent of two X. Raised to the power of acts. We're going to want to rewrite this by taking the natural log of both sides. Um and the reason why we do this is so we can rewrite it now as the natural log of your tangent of two x Divided by one over X. Now with this, when we take the limit we get negative infinity over infinity. So we're gonna have to use low tells rule. Taking the derivative of the top and bottom. We end up getting a negative two X squared second squared two X over signed to Acts over Crossan Q. Acts that allows us to cancel some things um and simplify further. Um Ultimately though, when we apply the limit will get the indeterminate form again. So we have to take the derivative one more time. And that will give us negative for X. Over to co sign two X. Now, when we apply the limit is exposed zero, we get zero. So we see that the natural log of Y equals zero, which means that why is going to equal one for the final answer?

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham