evaluate-the-limit-if-it-exists-lim-_x-rightarrow-2-fracx2-x6x2

Question

Evaluate the limit if it exists.
$$
\lim _{x \rightarrow-2} \frac{x^{2}-x+6}{x+2}
$$

Foster Wisusik · Accepted Answer

Okay, This question would like us to evaluate this limit. So, as always with these limit problems, we&#x27;re going to start just by directly plugging in. So to do this, plug in negative, too. And we get four plus two plus six for 12 on top, and then negative two plus two, which is zero on the bottom. So we know we have some kind of infinite limit or it doesn&#x27;t exist. So we need to test a point to sort of test the right and left hand limits to see if they match up. So we&#x27;re gonna test the limit as X approaches to her negative to from the positive side first. And we just care about the signs here. So if we have a number satellite Lee bigger than negative, too. We&#x27;re going to get a positive number on the bottom and then on the top, we&#x27;re also gonna have a positive number. So if we approach from the positive side, we have positive divided by positive, which is positive. Infinity. And then we did the same exact thing for the left hand side. So again the top remains unchanged because we have a positive plus a positive positive. Positive still and then But on the negative side or sorry. On the bottom side, we do get it negative because we get, like, negative 2.1 plus two, which is negative. So this sided limit is negative Infinity. So since the right side limit does not equal the left side limit, our limit does not exist.

Foster Wisusik · Answer

Okay, This question wants us to evaluate the following limit. And to do this, our first step should always be the directly substitute and see if that works. So if we do that, we&#x27;ll plug in to and get four plus two minus six, divided by two minus two. And if we do this, we get zero divided by zero. And that means it&#x27;s an indeterminant form so we can do something to this limit to find the answer, and we have a quadratic on the top. So let&#x27;s factor that quadratic to see if that helps us. So we have X squared plus X minus six. So we need to numbers that multiplied a negative six and add toe one. So that&#x27;s positive. Three and negative, too. And if we look here now, we have a factor of X minus two on the top and the bottom. So they divide out, leaving us with the limit as X approaches to of X Plus three, which plugging in, we get three plus two, which is five, and that&#x27;s all right

Amy Jiang · Answer

Okay, so we want to find her falling them about you. Let&#x27;s start by plugging in X is equal to negative two. So we have negative two plus two here. Do not seek with zero. So we have division by zero, so we can&#x27;t do that. Instead, let&#x27;s talk throughout our numerator. So in our new Raider we can practice into a exports two times X money stream. This is all over exposed to. We can counsel outer like Tim&#x27;s. Now it&#x27;s plug in our ex turn. So this is equal to negative two minus three, which is equal to negative five.

R M · Answer

number 10 a limit off extents off X spirited minus war X Let&#x27;s war over X brand lost X Wyness seats, which compete Simplify toe X minus two times X minus two over X training When buying text. My misdoing, which can be eliminated and we can subsitute using X, is equal to two. So the fund and enter for that and would be, as you know, over five, which is.

Matt Just · Answer

Okay, so you have the limit Specs approaching zero of six X squared cho tangent x times because he can&#x27;t two Max. Okay, if you don&#x27;t know what to do, you&#x27;re not alone is the mess. But the trick with all these trick functions is just to write them in. Terms of signing could sign as quick as possible. And I mean, our head years that we&#x27;re going to be trying to use sign X over X. That would be fun. So we want to write everything in terms of these sine x of Rex. So you have six x squared times. Contention is co sign X o ver sine x and then Cassie Kin is one over. Next Teo. Sorry. One over. Sign of two X Good. And now I&#x27;m going to take All right, there&#x27;s two exits here. I&#x27;m gonna divide by x squared. I&#x27;m gonna put one of the exit so and divide by x squared and dividing the numerator back screwed. Then I&#x27;m going to divide this by X squared. Goodbye, ex in this by X So then these x squared will cancel. No knows I&#x27;m not changing anything because I&#x27;m just We&#x27;Ll tow X squared divided by text about it. X just went and then I also needed to hear. But if I put it to here, I needed to hear. So I give it two here and two here. But now what&#x27;s going on? This is going to be going toe one, This is going to be going toe one, This is now gone. Okay? Co sign X. Thanks. Purchaser is going toe. Okay. And let&#x27;s not forget about this too. So that&#x27;s kind of a mess. But what&#x27;s left? We have six times. One over one times, one over. Don&#x27;t forget about this too. Right here. This too made this one to the two&#x27;s Still here we get three.

Issa Dababneh · Answer

All right, so in this video were asked to find them. Limit is exposed to 06 x squared times co tangent, X times, Corsican two x And we&#x27;re supposed to use the fact that the limit SK goes is euros. I, Katie, but by Kinko&#x27;s first thing we&#x27;re gonna do is we&#x27;re gonna try to manipulate what we have inside the limit. So reversible since we&#x27;re looking for something like sine sine X divided by X. So we&#x27;re going to try to convert court engine into terms of sided co sign. So we know that the co tangent is just courtside X divided by acts. So we have this right here, and we also know that CO seek out to Rex is just one divided by side. And then now we&#x27;re gonna try to split our six x squared in such a way that whatever we have inside the sign is going to be found in the numerator. So, for example, here we have sine X, So we&#x27;re gonna pull in X from that 66 square Here we are here. We have to act. So we&#x27;re gonna pull it two x from the six x square. So now we&#x27;re left with three times. Co sign X multiplied by X divided by sine X multiplied by two x divided by sine two wings. So we&#x27;re gonna take our manipulation. But we did right here. I&#x27;m gonna plug it in to we&#x27;re gonna substitute it in toward limit as experts to zero. So now we have three times co sign next multiplied by another way to write X divided by sine X We can write it as the reciprocal of sine X, divided by x So here we have one divided by sine X divided by X And again we can also do that same trick in right It&#x27;s two x divided by sine toe Xs one provided by signed two extra biotic Plato And now we take the limit as excuse to zero. So the three years of constant so stays the same Now coastline X as X goes to zero. This becomes one because if we plug in zero, we get one fear That denominator becomes one. But we have one divided by one So that also this one again Here we have Wonderful. It will be one divided by one which is again one. So we have three times, one times one times one. So our final and source of the limiters exposed to zero this three.

Problem

Evaluate the limit if it exists. $$ \lim _{x \rig…

Problem 21 Medium Difficulty

Evaluate the limit if it exists.
$$
\lim _{x \rightarrow-2} \frac{x^{2}-x+6}{x+2}
$$

Answer

Does not exist

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Does not exist

Precalculus Mathematics for Calculus

Grace H.

Kristen K.

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Precalculus Review - Intro

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James Stewart, Lothar Redlin, Saleem WatsonPrecalculus Mathematics for Calculus

Grace H.

Kristen K.

Michael J.

Joseph L.

James Stewart, Lothar Redlin, Saleem Watson

Precalculus Mathematics for Calculus