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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.

$ \lim_{x\to 1} \frac{x\sin(x - 1)}{2x^2 - x - 1} $

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02:27

Mengsha Yao

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

University of Nottingham

Idaho State University

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.

06:14

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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So we're gonna be finding um the limit of this value by using reptiles rule, the function is going to be X times the sine of X -1 provided by two, X squared- X -1. When you plug in one directly, we get 0/0. Since that is the indeterminant form, we want to take the derivative of the top and bottom. When we do that, we end up getting the sign of back plus one plus X, co sign Of X -1. And then the derivative of the bottom is just going to be for x minus one. Now, when we plug in one will end up getting zero plus one divided by three. So our final answer is going to be won over three.

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