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Question

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

Carlos Pinilla · Accepted Answer

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&#x27;t Minus infinity goes is here. So here you&#x27;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&#x27;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&#x27;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&#x27;s also about to Central Square Anything. I&#x27;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&#x27;s bullshit to mindless sex. Sees you didn&#x27;t mind sick. We have a factor of miners. One do the channel that&#x27;s mine was one because they&#x27;re sounding their function there. 96 It&#x27;s a little What I have is you. We&#x27;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&#x27;ll clean it up before your meeting or zero over. So we&#x27;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&#x27;s beauty. A great book to eggs, which is to no minus leaving 1 60 miles. You didn&#x27;t mind sex boating, and you get a factor of miners want due to ditch rule. So he&#x27;s gonna be That&#x27;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&#x27;re buying 18? I don&#x27;t know issue. So this limit we&#x27;ll be able to hear, as you can see here, the the exponential Let me be here because, uh, exponential moves gross. Plus, they&#x27;re not mention blues fluster Who&#x27;s faster than many going? It&#x27;s important book. What will you normal guest Exponential. The experiential wings In terms of really well, who was faster

Carson Merrill · Answer

the first problem, we&#x27;re going to be taking the limit as X goes to infinity of the function. Um So in order to do this one, we&#x27;re gonna want to take the natural log of both sides. And when we do that we can simplify it to be the limit as X approaches infinity of the natural log effect over E to the X. The reason why we do this is because now it makes it much easier to evaluate the limit. When we plug in X going to infinity, we get infinity over infinity. That&#x27;s an indeterminate form though. So we&#x27;re going to need to use local tells rule the derivative of natural log of X is one over X. And the derivative of E to the X is just to the X. Now, when we plug in infinity we will get here. One over infinity is zero. So it&#x27;s got zero and then each of the zero is one, Even the Zeros one. So we get one right here. But zero is not our answer. In fact, the natural log of Y equals zero is our answer, because we took the natural log of both sides. Now, when we solve for why we see that Y equals E. To the zero, which equals one, so one is going to be our final answer.

Carlos Pinilla · Answer

it&#x27;s we have here. Limit six goes through. Oh, the function of X. Who&#x27;s you before? One over? X My nose. Thanks. Over here. My six close impeding exclusivity They use s 00 here. So care for a baby? What was here? Get up. A sexy ghost in Haiti. Yeah, Use Goto zero. So you got one. But do you have Nitin? Hey, the so Well, What is it? So what we have to I need this expression just like that. Kind of tell for sure what it is, but also what be factor? The X. She&#x27;s gone there because he&#x27;s so well, it was well, the place. Oh, extents. You do one over X. Well, there six. That&#x27;s one. So minus what? I&#x27;ve really been like that. So, um, you have these And also this would be Oh, you need for unity this rule boat this year, So young. You mean other foreign gaby or zero. You can be turned into a Kocian. Oh, well, it&#x27;s X equal to dividing by one over X. So let&#x27;s be the one works on bottom. So this let me get a six course Kennedy look through one over X minus one invited, like one over X. So if you go ahead and try to Really, this means you&#x27;re gonna have something of a formal this year. But just one So one minus one bc over there. Well, zero. I&#x27;m not wanted a large number. Go zero. So we&#x27;re in good shape. Complying. Love you because you have farmed 00 so we can different shit play What? We built this expression so well. We appreciate that you want to buy the friendship. That so this is the awesome with one exponentially is the same exponential that now you have to supply people. One works with cheese. People don&#x27;t mind us won over picks a squirt because, well, one of your ex people to mix minus one Selected polar rule. Really friendship. These, uh, the miners comes here down, you know, minus then? Yeah. The four decreases by wants You get minus six to the extreme minors. To which my nose one works is squared there. You that I&#x27;m not well here. Is that your differentiate? Implicit function? All right, Dysfunction. Also, the one has Yeah, zero before walking into that. But it said so. My zero. You know, there was this is gonna be minus one over X quip. Great. So those through counsel from the well, uh, you can see that now we can go ahead and follow it to the limit. We only fr lease expression on top. So a sex go see if anything, these will go zero. So these expression will goto e borrow zero. She&#x27;s, uh, all that he&#x27;s won. So this lead a sequel to one ling. Yeah, but only visible to one.

Amrita Bhasin · Answer

first things first. Let&#x27;s rewrite this without the negative exponents. It&#x27;s easier to read now. We know that we have number and denominator both go towards infinity as X goes towards infinity. Therefore, we can apply the hospital&#x27;s rule. Therefore, take the derivative of top and bottom three X squared over two acts each. The X word you know you can cross off one X Therefore, we have three acts on the top over to eat of the X squared. Now we capture a pile hospital&#x27;s rule again In order to actually get an answer, we end up with three over infinity. Remember anything divide by infinity is zero.

Bryan Lynn · Answer

do we need to solve the limit? As X approaches infinity of X cubed times e to the power of native X squared. And so each of the power of negative X squared is really one divided by Ito power of X squared. So when we rewrite it in that form, so it would be the limit as X approaches infinity of execute over e to the power of X squared, Then we can he violate this limit. So let&#x27;s evaluate at infinity and we get infinity cubed over e to the power of infinity squared, which is, of course, infinity over infinity. So this means we can use Blue Beetle&#x27;s rule here and take the derivative. So let&#x27;s take the derivative, uh, both the numerator and denominator. So the derivative of the numerator being three x squared and the derivative of the dominator being two x times eat the power of X squared. You know, we actually get a cancellation, right? We can get rid of one of these exes us. This is going to be the same. Oust the limit as X approaches infinity of three x over two times e to the power of X squared. So we will evaluate again and we&#x27;ll get three times infinity over two times E to the power of infinity squared, which is infinity over infinity again. A solely used Loki tells Rule one more time or who knows how many more times, but at least one more time. And so that will give us the limit as exit, purchase and Fanny. Now you want the derivative of three X, which is three and then the derivative of two times each, the power of ex squares that&#x27;s gonna be It&#x27;s gonna be two times, two x times each part of X squared, which will be four times E to the power of X squared. Okay, so now we will evaluate the limit again, and in this case, we&#x27;re gonna get three over four times E to the power of X squared. But not an X ray. We&#x27;re evaluating it. So it&#x27;s gonna be infinity squared, which is equivalent to three over infinity, uh, which is gonna be equal to zero. So the limit is equal to

Mengsha Yao · Answer

Yeah, Okay, fine. That the limit us locked us rule there a proper great if they&#x27;re some are elementary. My third Consider using it. Okay, here is the limit as X goes to infinity. So if you&#x27;re plucking infinity to the cop log rhythm functional algorithm infinity, which is infinity. So you square it, Takis infinity. And he wanted by another run that another x x goes to infinity. So there&#x27;s this infinite he divided by infinity, which is saying determined the phone so we can use the locked house rule to write it as the limit as the axe goes to infinity that you&#x27;re a tip off that hop because two times Lok X, use the power rule force first and then use the train rule to find a curative off his side function that isthe one over X. And then he wanted by the curative off the denominator that hiss one. So, actually you just need to find the limit off this function and that his Seiko too. Since the limit has the linear property, you can put a truly in front that Islamic as X goes to infinity now algorithm function of X times where our ex that means this one divided by X. Okay, So here you feel plaque in infinity to here and here. That is also infinite. He divided by infinity, which is? They come in the form so you can use the love house rule again. Practice as the limit. A few times the limit has goes to infinity that the early if off the top fishes where our ex divided by the curative off the denominator like this one. So you get the limit as axe ghost waiting for that hero our acts that his zero so two times zero is zero.

Problem

Find the limit. Use l'Hospital's Rule where appro…

Problem 24 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..
$\lim _{x \rightarrow-\infty} x^{2} e^{x}$

Answer

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

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

Biocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Kristen K.

Joseph L.

James Stewart

Biocalculus Calculus for the Life Sciences