find-the-limits-lim-_theta-rightarrow-0-fractan-thetatheta

Question

Find the limits.
$$
\lim _{	heta ightarrow 0} \frac{	an 	heta}{	heta}
$$

Zachary Mitchell · Accepted Answer

We&#x27;re starting with limit as X goes to zero of tan of Excuse me, I&#x27;ve written x here, but I meant fate. Oh, 10 of data divided by Fada. Now, let&#x27;s go ahead and check to see if we can use low petals rule, um Or if we can just do this limit. So when we try to do the limited the numerator, we get zero try to do the limited. The denominator would get 0 0/0 We have an indeterminant form and we can use lobaton. Okay, some reading LH over the equal sign indicating that that&#x27;s the next step low Patel&#x27;s room. So the numerator we get, she can&#x27;t squared because the derivative of Tanis against weird the Trudeau of data is just one. And this is something we can evaluate. Lemonis one

Amy Jiang · Answer

Okay. I&#x27;m giving the limit. As data approaches, the Earl of tensions of video over data squared. I was cool. Tensions of three pit up. But you&#x27;re at this in terms of sign and co sign. So it gets limits as zero or did off, which is o of side over. Hello, Zainab. Vato. Okay, they&#x27;re squared. Coach engines is it&#x27;s the sign of three Keita over a co sign. They don&#x27;t. Okay, now it&#x27;s divide and multiply by 30 squared. So we get the limits of bitter over and better put you. So excuse me, assign three data provided by Dana. Okay, then. We also have one over coastline. They don&#x27;t sign of three data. We have sign of data Was fortunate. Here. We&#x27;re gonna divide that data, and then we&#x27;re gonna have three data squared over. Data squared. That to this limit is one. This is one as well. You stay. Just swear this cancel. We get close. I&#x27;m so close. And so that&#x27;s the secret one. So this is this equal to three

Issa Dababneh · Answer

All right. So this one street were asked to determine the limit of state of US 20 tangent. Frieda divided by data squared times court ended three feet. So the, uh, so remember first and we&#x27;re going to do is burn algebraic clean if you like. What&#x27;s on the inside of the limit, while keeping in mind that we should use the limit as X goes to zero off sine X divided by X equals. So since we&#x27;re gonna so first of all, what we could do since we&#x27;re gonna use we need to use the sign Live it that we know we&#x27;re going to convert attention and Cook Co 10 jin into sign and co son So tension Beta. So the fate of square we leave it the way it is. We know that engine data is just sign Say that divided by close I later and now co changing three feta is coastline. Three data divided Walker&#x27;s. However, since the co tension is in the denominator, What we do is we do we use the reciprocal which is co signed 33 divided by size, Bert. So first thing we&#x27;re gonna do is, well, little pull out the co scientist on the coastline. Three feet on the denominator. So we have one divided by coastline. Beta times. Go sign three data on the outside. And then now we have, uh, so we have co side square things. We&#x27;re going to split this coastline square. Uh, sorry. We have data. Swears that we&#x27;re gonna split this data squared into two. So we have a theater right here in the denominator in the theater right here. So we have science data divided by fate of which is great. And then here we have signed three sita divided by Well, remember, whatever is on the inside of the coast side has to be the same as that as what we have in the denominator. So here we&#x27;re missing the three. What we can do is we can both fired by for uber. So it&#x27;s it&#x27;s okay to multiply by 3/3. Because, remember, 3/3 is just one. So if you multiply something by one, you didn&#x27;t really change the expression. All right, so now we take what we did and the the algebraic manipulation. But we did, and we put it back in, you know, work, right? here for a sickle. But look at this. I have one divided by co sign beta times co sign everything all right, we plug in. Seeing growing to that, we get one divided by co sign zero times code signing three times years. So it&#x27;s one over coastline. Zero consequence lives here. What sign? Zeros. What? So that&#x27;s why and now the limit of spine data divide by Sarah&#x27;s data goes to zero is again one on a sign of three theater divided by three theaters. State of those 20 is also, but we have a three right here. Remember the balls of the finance. If you have a constant, you can pull it out. So this three got pulled out. And then now we have the limit of thes three terms. And like we said, this one is just 1/1. Just one the limiter stated was zero off 78 over theaters, again one and also the limit. As Theda goes to zero sign three theater divided by three data is also remember because what we have on the inside of three theater what we have on the inside of Sign is the same as that in the denominators. We have three data, both in the sign and in the denominator. So sometimes one times one is one. We have a three on the outside. So we have three times one and three times one is just three. So the limit as data ghost is zero is just three.

Amy Jiang · Answer

Okay, so we&#x27;re after the limit. As data about Giselle data coastline a bit. Well, what is the limit as their approaches over there? That&#x27;s just stop. And the letter as it approaches the coast Innovator, that&#x27;s cause I don&#x27;t know which one would it sell times one?

Issa Dababneh · Answer

So in this question were acid term. In the Lynette estate, it was 20 off. Eight attempts Coast. So you can do is we can plug in 0/4 ada, get zero times close side of zero. You know, that cool side of zeros? Just one. So we end up with zero times one best this year, so that limited.

Clarissa Noh · Answer

it&#x27;s clear. So when you read here, so we have the limit. State approaching zero. Sign Peeta over Data plus 10 gin. This is equal to when we convert it in terms of sign and co sign Tine over. Data was sign over. Go sign. We multiply both top and bottom by one over data and this gives us the limit. Must date approaches. Zero for a sign of beta. Over. Beta over one plus. Sign the data over. Data Arms one over. Co sign data. This equals the limit. State approaches zero. Signed data over Rita. Well, over the limit. Estate approaches zero. The one plus the limit. State approaches. Ciro. A sign Data over data earns the limit. State approaches zero. Everyone over co sign. You know, we get one over one plus one. Tell us. Excuse me. Multiplied by one over one. And this gives us one, huh?

Problem

Find the limits. $$ \lim _{t \rightarrow 0} \frac…

Problem 9 Easy Difficulty

Find the limits.
$$
\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}
$$

Answer

$$\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=1$$

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Calculus Early Transcendentals

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$$\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}=1$$

Calculus Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Grace H.

Catherine R.

Anna Marie V.

Caleb E.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals