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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} $

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01:48

Mengsha Yao

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Oregon State University

Baylor University

University of Nottingham

Lectures

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In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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$8-68$ Find the limit. Use…

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

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