what-happens-if-you-try-to-use-ihospitals-rule-to-find-the-limit-evaluate-the-limit-using-another--2

Question

What happens if you try to use I'Hospital's Rule to find the limit? Evaluate the limit using another method.
$\lim _{x ightarrow(\pi / 2)^{-}} \frac{\sec x}{	an x}$

Carlos Pinilla · Accepted Answer

you have to believe it. Six Postal left off number Fix. You got it right. Dungeon. So, uh, well, he&#x27;s yours. Why? I recall sign. So we&#x27;ll go. We&#x27;ll go to Infinity, then. Here. This close enough by house. This is you. The dungeon. Also feel completely because it&#x27;s gonna be a sign. Ex Oracle sign ethics. Which Littles who go to Haiti. Save me a plate. Um, I love you. We can do it too. I know, Huh? So differentiate it up. A little signal is, uh, did the pigs Signem. You have found your c squared squirt Also, uh, well done on the next thing you know, useful. That&#x27;s old Italian. So Well, these looks prison alerted that ordered, um is one of it up. So, uh, well, you&#x27;re playing over again. Think, uh, well, I&#x27;m saying it seek and over magic. So we&#x27;re but two step one where we started. Uh, so we&#x27;ll go. He&#x27;s No, it always Yeah, he&#x27;s here. Well, not always give you that. So what you can do is, uh, simplify these expressions. Yes, we have portions. Well, this is equal to one over co sign. Well, Becks, by the right sign of Lex over. Cool. Sign of X. Sort of these is equal to that. Is that well, these warrant fence post? Well, looks let him buy clothes and fakes fix. So that that she called you what? I just said that, uh, writing that out. So it seems you can you cannot veloute clean. It&#x27;s the school being These were just placing the function. So points So his body so well, it&#x27;s gonna be able to believe, you know, sex equals two helps from the left. Hope Just one over a sign off, bex, but physical more about those one one over one, which is one

Bryan Lynn · Answer

All right, so here we are, given the limit as X approaches Infinity, Uh, X over the square root of X squared plus one. And when we try to evaluate this, we get infinity over infinities. So that means we should be able to use local tolls rule. And we When we try to do that, we take the derivative of X. That&#x27;s just gonna be one. The derivative of the square root of X squared plus one is going to be X over the square root of X squared plus one. So this is going to be equal to you. Limit as X approaches. Infinity of the square root of X squared plus one over X. Okay, well, again, says the universal of what we had before we evaluate and get infinity over infinity so we can try a lo pee tos rule again and we&#x27;ll get the limit as X approaches Infinity of again. The derivative of the square root of X squared plus one is going to be X over the square root of X squared plus one. And we put that over the square to Baxter just one. So we get the limit as X approaches infinity of X over the square root of X squared plus one. Well, this is what we started with, right? So that&#x27;s not really helpful. We could keep applying low Beatles rule forever until the end of time. Um, and won&#x27;t get anywhere. So we need to do something else. Seward antique. This fraction that we&#x27;re taking the limit of as X approaches infinity, the square root of X squared plus one. And we&#x27;re gonna divide by largest power central. Multiply by one over the square root of X squared over one over the square root of X squared. So this is the same as multiplying this by one. And when we do that at the square root of X squared is just X. So we turn the top into a one here. And then since we&#x27;re dividing throughout here by X squared, we end up with ease. Square of one plus one over X squared. They forgot to write on women. It just get excited here. Because now when we evaluate the limit, this is going to be equal to one over the square root of one plus one over infinity. All right. We can treat one over infinity like zeros. That&#x27;s one over the square root of one or simply one, and then not is our limits so well.

Amrita Bhasin · Answer

okay, If we try to use the hospital&#x27;s rule to evaluate this limit, we see that we end up with something strange, which is that we end up with the same thing that we started with flipped, as you can see. Therefore, we know we have to rewrite the limit and manipulate it in a different way. So usually, when the hospital&#x27;s rule doesn&#x27;t work, you have to manipulate the limit. So let&#x27;s put the whole thing under the square root so the derivative of the top is too accident expertise to exit and then derivative of X squared plus one is two acts. The post one just goes and derivative of zero, which we don&#x27;t even have to acknowledge. This gives us the squared of one, which is simply one right, because the trucks on top and chips and one cancels

Linh Vu · Answer

limit under second under. Thanks. Are, uh, benching him, toe. Thanks and thanks. Yes. You know, pie and a Jew from the left on here. When? X ketchup. I entered you from the left. We have this one. We&#x27;re hand of fun on the infinity have Ah, infinity. And then if we tried to use in a little Britain room here, let&#x27;s say what we&#x27;re going to happen here. Okay? So have a limit. Excuse your client to from the left and now a rift in the second encouraging a second tension moved in attention. It could, you know, second square on the X. And now and we try Jersey undefined. And we get this second concern with this one, and then we get back gender flip over on the Braves won here, And if we keep doing so, you should get back and falls again. The fever of under tension And the second So it&#x27;s not the best way to a planet. Levitan wrote in this case now, however, and we tried to modify this a little. So limit execute you by Joe from the left. Second we know isn&#x27;t good. You one never go sai. I&#x27;m that Thanks your intention, it could of course, I X over. So thanks. Therefore, we get a limit on the experience to buy into two on the left off, Uh, se x of Ah, because I square X now is a time job, man Levitan room now because we have the farm under on one. Uh, no, it&#x27;s extra Jew, but up to the top one bottom having zero. Therefore, we had little echo to ah uh, one development infinity here.

Carson Merrill · Answer

Yeah, this problem, my hair, we&#x27;re going to be using what cows rule to find. Uh the limit of the function. Natural log of X. Get that uh times the tangent. So we&#x27;re going to do over the co tangent of X. High over to. So that way when we plug in one plus we end up getting a negative chew over pie. So in this case we don&#x27;t need to use locales role as long as we convert it to this form right here, once we plug in the one here we&#x27;ll get pi over two. Um And then this will be uh Approaches one from the right, we&#x27;ll get Natural Log of one. So this is through taking the derivative here. Actually we do have to take the derivative because we get 0/0. So that&#x27;s one over X. And then this is going to be negative coast second squared uh exp I over to you Time high over two. Then when we plug in one we would get two divided by a negative high

Carson Merrill · Answer

for this problem. We&#x27;re going to be taking the limit as X goes to one of two, X minus one to the tangent kayaks over to. We&#x27;re gonna want to take the natural log on both sides. So to make things a little simpler and when we do that, we&#x27;re going to end up getting um the natural log of q minus X Divided by co tangent of high x over two. So now we can evaluate this at x equals one. Um but we&#x27;ll get 0/0 the indeterminate form. So now we&#x27;re going to use locales role. We&#x27;re going to take the derivative of the numerator and we get one over to mine attacks. And then we&#x27;re gonna take the derivative of asking me a negative actually. And we&#x27;re going to take the derivative the denominator and we end up getting a negative coast sequence squared. Okay. Hi X over two times. Hi over two as a result of this. When we evaluate it we end up getting chew over pie. But remember that that is the natural log of Y. Yeah. Equalling two over pie. So our final answer is going to be E to the two over. Hi, for the final answer.

Problem

Models of population growth have the general form…

Problem 48 Medium Difficulty

What happens if you try to use I'Hospital's Rule to find the limit? Evaluate the limit using another method.
$\lim _{x \rightarrow(\pi / 2)^{-}} \frac{\sec x}{\tan x}$

Answer

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sec x}{\tan x}=1$

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$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sec x}{\tan x}=1$

Biocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Caleb E.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Caleb E.

Michael J.

James Stewart

Biocalculus Calculus for the Life Sciences