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Find the limit. Use I'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.$$\lim _{x \rightarrow 1} \frac{x^{2}-1}{x^{2}-x}$$

$\lim _{x \rightarrow 1} \frac{2 x}{2 x-1}=2$

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

Differentiation

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All right. So here we were, given the limit as X approaches one X squared, minus one over X squared minus X. Right. So we will evaluate it this fraction where X equals one. And what that gives us would be one square, minus 1/1, squared, minus one, which, of course, 0/0. So we can use Lupita. Lt's rule. Now, the states that we will give take the derivative of the top over the derivative of the bottom. This is gonna be equal to the limit as ex church is one of two X over two X minus one. So now we can do the same thing. Evaluate The limits will put one in, and we get two times one over, uh, two times one minus one, which, of course, is equal to 2/1. And that is equal to two. So the limit then of this is going to be too

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