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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} x^3 e^{-x^2} $

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01:30

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Campbell University

Oregon State University

Idaho State University

Boston College

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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first things first. Let's rewrite this without the negative exponents. It's easier to read now. We know that we have number and denominator both go towards infinity as X goes towards infinity. Therefore, we can apply the hospital's rule. Therefore, take the derivative of top and bottom three X squared over two acts each. The X word you know you can cross off one X Therefore, we have three acts on the top over to eat of the X squared. Now we capture a pile hospital's rule again In order to actually get an answer, we end up with three over infinity. Remember anything divide by infinity is zero.

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