evaluate-each-limit-if-it-exists-use-l-hospitals-rule-if-appropriate-lim-_t-rightarrow-infty-fracln-

Question

Evaluate each limit (if it exists). Use $L$ Hospital's rule (if appropriate).
$$\lim _{t \rightarrow \infty} \frac{\ln \ln t}{\ln t}$$

Carlos Pinilla · Accepted Answer

So we have a limit. Thio, We&#x27;re still cereal off the fortune Do the three times t my house one over, teen. Also, if we were to just know goes trading by the limit, we couldn&#x27;t do it because be dividing. There&#x27;s something that both zero is gonna go. So zero I&#x27;m not. So you could get the top or this will go to 111 Cyril. And then you see, uh, that, uh, we have ah, I won&#x27;t go. We&#x27;ll be those form, which is one of those is Cyril or zero. So apply love it&#x27;ll you need to have. You&#x27;re, you know, Are you need off the farm? Zero over zero. Who are you? But what? We&#x27;re in this case in the breeze you over zero. So we&#x27;re gonna bull head on a plate. Woe. Um so little does Is these limit people limit I do this in place. Studios two off these function on top differentiated. You think they do that function over the function on bottom. So with this prime, I mean differentiate that function so as you know Well, uh, maybe friendship on exponential the we&#x27;ll just get the same exponential, but the this power from zone. So you&#x27;re gonna get where the general I tell you, needed free team. But, uh, that she comes down because you&#x27;re differentiating this inner peace with a tip off. Three Teen, these three. So from that, But like the channel there, you give the three on the Red Eagle one. Whoa. These that move across town zeal that I&#x27;m not. We&#x27;ll be ready. He just won. So you get these form now? We&#x27;re here. Good shape. Do just good place. Let&#x27;s see Diego&#x27;s That is not an X 13 sideways. She looks like a Mexico city. Uh, so you can just go ahead and plug in people&#x27;s heroes. You&#x27;re gonna get three times. People are zero right over one. Our bodies you could issue is one. She just get three through one, which is

Bryan Lynn · Answer

Okay, so here were given the limit as T approaches area five to the power of T minus three to the power of tea over tea. So first we will evaluate At T equals zero. We get five to the power of zero minus three to the power of 0/0. This is gonna be equal toe one minus one over zero, which is 0/0. So that means we can use low petals of rules. But we have this 0/0 happening, and when we apply that, we will get the limit. As T approaches zero, we want to take the derivative of the top, which is going to be five to the power of tea. Natural, either. Five minus three to the power of tea. Natural lot of three over the derivative of the bottom, which is going to be equal to one. Okay, so now we can try to evaluate the limit again. Um, And when we do that, we get five Ellen five 50 natural. Have a five minus three to the power zero. Natural are the three. And ignore that bottom part of the fraction. And so this is gonna be equal to the natural log of five minus the natural log of three. Okay, well, this using our rules of law algorithms is really gonna be equal to the natural lot of 5/3. And there we have it. That&#x27;s going to be

Bryan Lynn · Answer

Okay, so here we have the limit as X is a approaching zero of B to the power of T minus one over t cute. And so first, we will simply e evaluate the limit. Course. I already made a small typo that should be 80. Otherwise, this doesn&#x27;t make any sense. So first will evaluate the limit, will put t equals zero in there and see what we get. She would get eat. The zero minus 1/0 cubed, which would be one minus 1/0 is 0/0. So therefore Lotito&#x27;s rule applies. We&#x27;re gonna take the derivative with respect to t of the top over the bottom and take that limit instead. All right, so the limit of U to the T minus one is going to remain just e to the t and the one has been dropped out. And then the derivative of tea to the power of three will be three t squared. So now we&#x27;ll try again to simply evaluate the limit At T equals zero. And when we do that, we get eat of the power of zero over three times zero squared, which will give us 1/0. No, no, we have not a 0/0. This means that our women is going to be infinity. This one is getting divided by tinier and tinier numbers, which means the resultant numbers are larger and larger and larger. Eso this limit is equal to infinity.

Carson Merrill · Answer

so we can either use the reptiles role or not use the hotel&#x27;s role. Um In this case it&#x27;s much easier to use low petals rule because we see once we plug in zero we get 0/0. And it&#x27;s often trickier to deal with exponential functions and triggered a metric functions. So in this case we&#x27;re just going to use um lovely calle&#x27;s role. So we take the derivative of the numerator and we get to e. The two T. We take the derivative of the denominator. Um The derivative of sine T. Is co sign T. So we do that. Now this allows us to evaluate the function at T. equals zero. So when we do that this is going to end up giving us as a result. Um two E 20 which is one Provided by the co sign of zero which is so to eat of zero is going to be two times one rather. And then coastline of zero is just one that&#x27;s going to end up giving us two divided by one. Which is to and that will be our final answer for love. Cause a real problem

Carlos Pinilla · Answer

So we have a limit. Essam, you goes through with a function? Yeah, to the bar. You You&#x27;re right. 10. Or you borrow three. So Well, if you go ahead and just plug you Yes, you go safe for all of you. Wait. 10. That&#x27;s gonna goto well where he goes. Exponential wolves? Definitely. So? Definitely. So you you was gonna go if you are. Time&#x27;s gonna goto. Verity. I&#x27;m Dana Borromeo also grows. They finish you okay? Indefinitely. So he&#x27;s gonna go to you lately, So we&#x27;re in good shape applying. Let me go. Well, you don&#x27;t, and so will we. You can go ahead and different ship dysfunction. One of the friendship Exponential. You get the same explanation, but, uh well, be careful there. Here you have. Ah, on our function will you compose him inside the expansion, which is? You did it out. So you get a fuck off. I want them additional special. So these would be this. But it is inevitable. You you over. So don&#x27;t eat it. You the either you were 10 time&#x27;s. One thing you overcome bonded with the friendship, the water All the power comes own. It comes on their plane when you lower before by one. So you get three times you squared. Well, this squared is 3,000,000 won. Um, So what rule tells you that she&#x27;s leaving Will be exactly the same. Was that lead chair or obviously terrified? There are the community in us. Yeah, you We can when you send you 10 on bottom times. Three years old. Three times. Stan, That&#x27;s Trudy. Comes, you squirt. Well, let me fix you. Still may be, uh so as you can see here, uh, yet plugging because I would have she goes there, baby, he&#x27;s gonna go to infinity in under three Times Square. We&#x27;ll also go to 30 times Your score&#x27;s gonna go 30 times infinity halting TV. So we&#x27;re also you love it. So Lovato framework, uh, so we can apply looking again. So when you differentiate this expression on top, you&#x27;re gonna get Yeah, you advance times wanted begun. Chiharu from the Times 30 on the power Here comes own. So it&#x27;s ready. Times two the four of you decreases by one. So So it seems you won so putting off their those one over. Well, then 60 three times 36 So you get um, one of their six hundreds, uh, e b b you dense or you. But at this point, you just brilliant. Then you&#x27;re gonna have the form here. Well, that&#x27;s gonna go to Katie you Folsom Treaty. So we need to play lobby till again. So this limit will be brutal. One word, six Science. You can put that order willing. It lead us. You those to infinity. Oh, you today, you over 10. Do you dance? Men were beautiful in shit piece. You get more than facto wanted. I&#x27;m there. Well, there are two of you. So these guns, or did I read? People Get up. I&#x27;m gonna forget their water off the bottom. They&#x27;re illegal fuel. Just, uh, what is one? Um, is gonna be one over 600 stance, then. So one of her six thousands, but, uh, So you go see if any titties over water help. Is there being on the bottom This girl boy? Either way, So you want to get beat? Well, you&#x27;re gonna be in a water hole. How many thousands longer. It&#x27;s it is final. No. What? You got to clear the air. Well, the morale of these long story should be, Huh? Uh, in the exponential Rose Foster, Go around. Not a play on. I don&#x27;t want a ho peak. So you have your reporting on you Bottom and exponential Will&#x27;s work faster. So these will our impunity this world were ween the bottle. Which function goes faster? Does getting you that, uh, the lead issue goes to Haiti? Those fools, You can&#x27;t have that expression.

Problem

Evaluate each limit (if it exists). Use $L$ Hospi…

Problem 30 Easy Difficulty

Evaluate each limit (if it exists). Use $L$ Hospital's rule (if appropriate).
$$\lim _{t \rightarrow \infty} \frac{\ln \ln t}{\ln t}$$

Answer

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus