Problem

Use l'Hospital's Rule to help find the asymptotes…

07:17

Problem 36 Hard Difficulty

Use l'Hospital's Rule to help find the asymptotes of $f$ . Then use them, together with information from $f^{\prime}$ and $f^{\prime \prime},$ to sketch the graph of $f .$ Check your work with a graphing device.
$f(x)=e^{x} / x$

Answer

$f(1)=e$

Related Courses

Calculus 1 / AB

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Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

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Video Transcript

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Excuse me, I'm no minus through them's x Times X Some miners in time sex squirt from now. Mindless minus blast. Blix waas True eggs Hold that devotedly extra for So was because you here we can counsel powers. Thanks to these four, all this is multiple effects. We can cancel one bar backs, so that sort of these become 63rd. This poor becomes just to that square is gonna be Except these will be just the constant, too. So a little prime sequel to E Through the X terms X squared minors to X plus two. You know that divided by Thanks, cube. So if you look at these, we want to find out the signs were of all prime. So this, uh, you tried to fuck for this boy? Oh, no. So use the is one is still you still say we're gonna do minus B plus or minus the square, which will be for port sequence of minus square minus four times. That was that. Eat them. See? So too thems for But as you can see here, well, these would be a negative brute. Um, so it has. No, it has no solution. That means that these is a problem. But he's always about the exactly. So So it's positive. This part is always positive. Or so it's positive. And this is the only piece that determines the sign for a little break so that if the brain will be negative for Xnegative, as you can see, there, I'm excused for explosive will be. So these stocks of all they uncovered it. So we have Ah, he's in for mention. Yeah, or derivatives. So we know that lease for mission. As you can see, uh, the limit doors you under from the right severity from the left His minutes pretty miss a function that is increasing or ex You know, one and a cute The Christian works is more no one And also you know that he's gonna give up works positive compete down Could give a damn for X We know the example. Lesson goods. So the function x very but x a point of reference. So what is it about? One? One would be just a ready one. So it would be you, not the point board one. Hey, I'm well, we know that the function from one on greasy in from one words greasier on before re secreting delimit years. And you know also that believe it Here six goes through minus infinity zoo set up. He's gonna yourself into that music cuisine votes so it should look something about, uh so I can keep up here. I can't get down there. So the function should look something like these.

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