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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
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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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