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Problem

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

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Problem 35 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_{x\to 0} \frac{\ln (1 + x)}{\cos x + e^x - 1} $


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Mengsha Yao

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

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Differentiation

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Problem 92

Video Transcript

Okay. So we see with this problem here we're going to be using reptiles role. It's the natural log of one plus X. And then that's going to be divided by the coastline of X plus me to the X. And this one. So with this in mind we realized that when we plug in zero, we don't actually get an indeterminate forms. So we won't have to use low tiles role in this case Plugging in zero. Here we get the natural log of one plus zero, which is just zero Plugging in zero. Here we get one, 1 -1 is zero. So that will go away. But then down here E to the zero is one. So the final answer is going to be 0/1 which is equal to zero. zero will be the final answer. So this problem that is the limit as X approaches zero of the given function.

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Video Thumbnail

06:14

Review

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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