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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
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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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