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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.$\lim _{x \rightarrow 1} \frac{\ln x}{\sin \pi x}$

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

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

Differentiation

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So you know, we're married. Six goes to one over function. True. You're a little more X over the function, son. But it's so if you go ahead about just plugging in, no principles. One you did well for literally move one. Uh, well, that's gonna be there, Is you? I'm done. Sailed by. It's also well, by X six goes to one is gonna goto. Bye. What? So we'll sign off any multiples off. Bye. It's also zero. So here you have the bar form zero over zero. So what, we're you can apply? Well, until from 00 you got, buddy, I love you. Still. So the rule tells you that this limit will be equal to the limit for six groups, too. It's in a place that doesn't change, but, uh, here, you can compute, really need off the developed those functions. Fortune dope differentiated deflection on bottom fart jokes. The people that well, so there are people not Rollo. We're roomies on the works. I'm the only thing sign is vehicle sign. But you need to be careful here because, uh so the argument off sign here, we that one of the function body X she needs a flight. Oh, the cheryl differently. That's you get, huh? Times the off by X, which is all right. So there you go. Tow the least limit. Then you know this fortune or the function. Six of one. So what's exhaust? The warm we're gonna up here on top. One of her one is one. And of course I buy mind as one. So one or when it is one thumbs. Bye. No, also, this is the same Waas. This is the same one. Minus one were. But so here you're able to play what we tell Because we have that form here. Over here, living this minus one or but

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