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Numerade Educator

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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

$\frac{1}{3}$

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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.