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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 1^+} [\ln(x^7 - 1) - \ln(x^5 - 1)] $

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02:01

Wen Zheng

01:05

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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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Find the limit. Use l'…

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Find the limit. Use I'…

So this problem, we're gonna be taking the limit as X goes to one from the right of the following function. Since it's a natural log function and it's using subtraction, we're going to turn it into a division by the The property that natural logs have. So the function now is going to be X to the 7th minus one um divided by actually faith except fifth, that's one. And keep mind this whole thing is the natural log of all that. But thankfully with limit, we can move the limit inside and kind of forget about the natural log for a second. Then when we do this we would get a determinant form. So we have to use local tells role. Once we simplify it further, we end up getting this down to 7/5. Yeah. Mhm. So the final answer, we can't forget about our natural log. So the final answer is going to be the natural log of 7/5.

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