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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 \infty} \left( 1 + \frac{a}{x} \right)^{bx} $

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02:31

Wen Zheng

01:13

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

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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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here we want to take the limit as X goes to infinity of the function. The function we're given is one plus A over X to the power of the X. So then we can take the natural log of both sides and simplify further. Want to get us um we'll end up having be times natural log of one plus A over X over one over X. Which allows us to let T equal one over X. So we'll replace this here will make that 80 and now T is going to be approaching zero instead of X approaching infinity. That's going to give us an indeterminate form. So we'll use the hotel's rule giving us a B Over one plus 80. Now when we plug in T approaching zero, we just get the natural log of Y equals A B. So why is going to equal E to the A. B. Final answer?

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