Problem

Find the limit. Use l'Hospital's Rule where appro…

01:14

Problem 36 Medium Difficulty

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} $

Answer

$\frac{1}{3}$

More Answers

02:27

Mengsha Y.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Discussion

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Missouri State University

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Video Transcript

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.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Michael J.

Idaho State University

Joseph L.

Boston College