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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\sin(\pi /x) $

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01:38

Wen Zheng

00:32

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

Baylor University

University of Michigan - Ann Arbor

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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Mhm. The first problem we're gonna be taking the limit as X goes to infinity of the following function. That's gonna be X. Sine of pi Uber X. So X sign of high over X is going to be our function. Okay? So when we substitute one over X for thi this is just gonna be pi T. And we know that as X goes to infinity to equal zero. So we can just change how we view the limit. So in this case now um this is gonna be a sign of pirate T over T. When T goes to zero now we have 0/0. That's an indeterminate form. So we'll take the uh derivative of the numerator. That'll be high co sign right? And this will just be one on the bottom. Then what will end up getting as a result is high time to co sign of zero which is one Over one. So our final answer will be high.

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