Problem

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

01:13

Problem 15 Easy 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_{t\to 0} \frac{e^{2t} - 1}{\sin t} $

Name: find the limit use lhospitals rule where appropriate if there is a more elementary method consider 8
Uploaded: 2021-05-27
Duration: 1 min 18 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_{t\to 0} \frac{e^{2t} - 1}{\sin t} $

Answer

This limit has the form
$\frac{0}{0} \cdot \lim _{t \rightarrow 0} \frac{e^{2 t}-1}{\sin t} \stackrel{\Perp}{=} \lim _{t \rightarrow 0} \frac{2 e^{2 t}}{\cos t}=\frac{2(1)}{1}=2$

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Missouri State University

Caleb E.

Baylor University

Michael J.

Idaho State University

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 we can either use the reptiles role or not use the hotel's role. Um In this case it's much easier to use low petals rule because we see once we plug in zero we get 0/0. And it's often trickier to deal with exponential functions and triggered a metric functions. So in this case we're just going to use um lovely calle's role. So we take the derivative of the numerator and we get to e. The two T. We take the derivative of the denominator. Um The derivative of sine T. Is co sign T. So we do that. Now this allows us to evaluate the function at T. equals zero. So when we do that this is going to end up giving us as a result. Um two E 20 which is one Provided by the co sign of zero which is so to eat of zero is going to be two times one rather. And then coastline of zero is just one that's going to end up giving us two divided by one. Which is to and that will be our final answer for love. Cause a real problem

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Problem