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

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01:06

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

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

04:35

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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Find the limit. Use l'…

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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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