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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..$\lim _{x \rightarrow-\infty} x^{2} e^{x}$

$\lim _{x \rightarrow-\infty} x^{2} e^{x}=0$

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

Differentiation

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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so I want to look at believe it. Six goes to miners and ability off excess squirt TVX Uh, so you just Oh, him again. You know, the squared. Well, those two immunity, But you didn't Minus infinity goes is here. So here you're You have, ah, two functions. Oh, well, our fortune became reflection growing. So what is? Okay, Zero. So you have to money pull it this expression to be reading to a form. But he's What should a bill suitable toe with But the the living ah idea should be that the exponential she, uh, should win. So this one is what should lead the behavior. That let's make that idea more precise. So you have this. 03 ex people toe. Go on over to the minus X. Right. So what we can write? These is a Georgian X squared, divided by might have sex. So, uh, well, if you look at the dealing it now in this far wall, this is getting change all that. It's also about to Central Square Anything. I'm not here minus minus. Infinity is gonna goto. Faith is about give the form you can be or in treating, huh? So we have a well, you know, farm figure completed so we can apply Lobito to this expression. Oh, so we dad, either fine shape his fortune or different shaving that function. So if you do that older, it will. Because quarries works under that's bullshit to mindless sex. Sees you didn't mind sick. We have a factor of miners. One do the channel that's mine was one because they're sounding their function there. 96 It's a little What I have is you. We're going at this point. Well, you have, uh, minus very being full time, baby. Well minus infinity to the minor sex goes to she gets so began. Not something off the farm. If you did. You ever see a d so will begin a right pickle again because we are. You know, the only lead off the front video are leaving. So you always always make sure that the I'll clean it up before your meeting or zero over. So we're in good shape till my lovely bones old definition that or that not leave it will equal toe the limit. Well, the argument here of the loot where X is going to 1000 change explosive one's beauty. A great book to eggs, which is to no minus leaving 1 60 miles. You didn't mind sex boating, and you get a factor of miners want due to ditch rule. So he's gonna be That's people till two. We find the minuses six, which is, people tone Well, six would want both. One is impunity. Well, all these girls school minus infinity minus ones in these woods everything. So you go slow if you issue a bottom. Well, that too. Stay still. Divide. You're buying 18? I don't know issue. So this limit we'll be able to hear, as you can see here, the the exponential Let me be here because, uh, exponential moves gross. Plus, they're not mention blues fluster Who's faster than many going? It's important book. What will you normal guest Exponential. The experiential wings In terms of really well, who was faster

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