guess-the-value-of-the-limit-if-it-exists-by-evaluating-the-function-at-the-given-numbers-correct-18

Question

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
$\lim _{x \rightarrow \pi^{-}} \cot x$

Paul George · Accepted Answer

everybody. Chapter two, Section three Problem 34. This one won&#x27;t take too long. This one is a snap. So we&#x27;re talking about Ah, the limit as X approaches Pi fromthe left of co tangent of X. So the most important thing that you need to know about this is that CO tangent is co sign over sign And when we have sign at pie, that is zero. So we have co sign of X over sign of X when you&#x27;re at pie, right? Satoko san. A pie is negative. One sign of pi zero You have negative one of zero so undefined, which means that you have a vertical ass in tow, which means that at this value of pi rights were blowing up. And if we&#x27;re approaching it from the left, which is what this minus means, that means that where were blown up, we&#x27;re either gonna blow down or we&#x27;re gonna blow up, and I need to know which one. So if we&#x27;re just a normal coach, Hank, a graph, if we&#x27;re blowing up, were positive. And if we&#x27;re blowing down, we are negative. So all I mean to dio is I need to find something that is just a little bit less than pie, and I need to find out if it&#x27;s positive or negative, and then that will tell us the story. So let&#x27;s plug in something that&#x27;s less than pie, which is about 3.14 So let&#x27;s plug in like 2.5, right. We need to get in between discontinuities, and there&#x27;s another just continuity at zero. So we just need to make sure to be in between zero and pi so that we can get an accurate read out of this thing. And so I want to. I want to be a pretty close to pie. Make sure we don&#x27;t jump over, you know, any access. So if we pick something like 2.5, right, let&#x27;s pick something that&#x27;s really, really, really close. Then if we plug into a 0.5 to this thing, we get co signed of 2.5, and keep in mind that I am gonna be doing this in radiance because it&#x27;s talking about pie. So I want to do this. It radiance. So if it&#x27;s gonna be in the bottom, we need a negative. It&#x27;s gonna be the top When you deposited Phillips it would get if you plug it into a calculator and you get co tangent. 2.5. Then you get something that is approximately negative. 1.3. And so that&#x27;s a negative number. So that means that it here, we live in a negative space, which means this thing is going to go down. And that means that the limit of this thing is we go from the left side is going to be negative. Infinity! There you go. Help that help until next time.

Bobby Barnes · Answer

We want to determine the infinite limit. Oh, as X approaches to pie from the left of ex Cosi connects. So I went ahead and did this by setting up a chart. So from the left means we want to plug in values that are smaller than two pi into here and so noticed as we go down, the values become extremely negative after a while. So we would suspect that this would go too negative Infinity.

Bobby Barnes · Answer

we want to guess the value of the limit of ex approaching three from the right of natural log of X squared minus nine by plugging in values that are slightly larger than three. So over here I went ahead and made a chart in Excel doing just that. And you can notice, as we get closer and closer to three, the value just become Maur negative. And if you were to just keep plugging and more zeros and getting closer to three from the right, then this would just keep getting more and more negative. So we might guess that the limit of this would be negative Infinity.

Bobby Barnes · Answer

we want to guess the value of the limit if it exists by evaluating our function here at all the values they ask us to now, one thing. I think there&#x27;s a typo in this question. Uh, I believe the denominator should be X squared minus X minus two, because otherwise checking with the answer they give in the back of the book gives something completely different from what we would get from the original one. So that&#x27;s why I went ahead and made that substitution of replacing that extra negative X with negative, too. Because otherwise we wouldn&#x27;t get what they have in the back of the book, Right? So I&#x27;m gonna head in, just made a Excel spreadsheet to help What&#x27;s with this? So as we approach X for two from the left, it looks like the values are getting kind of like 0.666 and then from the right, it also looks like it&#x27;s going to 0.666 So we might make a guess that this is just gonna be 0.6 repeating or two thirds. So this here is what we might make to be our guests of the limit as X approaches to of that function that we have up there

Paul George · Answer

everybody. So we&#x27;re working on chapter two, Section three, Problem 36. What we&#x27;re trying to do is we have a function of X squared minus two X over X squared minus four X plus four. Ah, and we&#x27;re trying to find the limit as X approaches to from the left. That&#x27;s what That minus a pin the top right corner to means If it didn&#x27;t have that, it would just mean from both sides if it has a minus, it means from the left, but a plus, that means for the right. So, ah, if I&#x27;m trying to do something like this, I try to simplify it as much as I can. So, um, because we&#x27;re gonna be evaluating this. But ex out of both parts, I know that and I could also sell the bottom that&#x27;s just X minus two squared, and then you&#x27;ll see that the one of the top cancels with one of the ones in the bottom. And you are, and so that means there&#x27;s a whole incident. You have exit over X minus two. And so what? That looks like. I don&#x27;t know exactly what it looks like, right, But I have a graph and I know that there&#x27;s a vertical ass and towed at two. I know that. I know that time the issue with like as you&#x27;re taking the Limited&#x27;s X approaches to some stuff is gonna happen. It&#x27;s gonna be one of, like, four different scenarios. Either it&#x27;ll jump. I guess we only care about the left, right. It&#x27;ll either go, you know, up like that, in which case the limit will just be infinity or it&#x27;ll go down. Ah, and the limit will be negative. Infinity. So Ah, and we don&#x27;t really care what&#x27;s happening for the right side. If it was from both, we would. But we don&#x27;t. So if I want to just plug in a value right, I&#x27;ll tell again. You know, like one. What&#x27;s the all you want? So be pulling in one. You get one over negative one. So the answer is negative. One so looking. You know, one guy&#x27;s right there. So I mean, it could crawl up from the bottom and, you know, it could look like this. It could look like that. So it&#x27;s not enough information quite yet. Um, but ah, if we look at the horse on ice until with this thing, it&#x27;s X over X minus two. So that means that the, um it&#x27;s even to the horseman lasting totals that X equals one. That means it&#x27;s right there. And so that means for me. If I have a horizontal es en toda there, that means I&#x27;m either gonna be trapped up here, or I&#x27;m gonna be trapped down there. And if you let me go to that trash, if I&#x27;m down here at one common negative one, that means that my graph has to go down like that. And then it&#x27;s gonna go like that because you can&#x27;t cross. Ah, horses. Last minto. I mean, you can sometimes this sense you want, we&#x27;ll talk about more like that later. Ah, but I mean, this is what the graphical look like. You could plug in 1.5. You get negative three right there. You&#x27;re down here. If you&#x27;re looking at 1.8, you get negative. Nine is so it&#x27;s part of the shares that it&#x27;s working. So if we&#x27;re wanting the answer right, the limit as X approaches two from the left of this function, which is equal to X over X minus two. That&#x27;s just equal to negative infinity. And try and clean that up. All right? What the help till next time

Bobby Barnes · Answer

we want to determine the infinite limit as exit purchase two from the right of irrational function X squared minus two Ex My state pullover X squared minus five X plus six. One thing that may help us is if we were to factor each of these. That way we can figure out if it&#x27;s going to be positive or negative coming from the right so the numerator should factor too. X minus for X Plus two and the denominator ship factor too X minus not too much issue, but X minus two X minus three. Now notice if we were to come from the right well to minus four, well, that&#x27;s going to be negative. Two plus two. That&#x27;s going to be positive as we approach to from the right of ex brightness to that should be positive and then X or two minus three would be negative. So overall, those two negatives would cancel out. So we might suspect that this would go to positive. Infinity

Problem

Determine the infinite limit. $$ \lim _{x \righta…

Problem 34 Easy Difficulty

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
$\lim _{x \rightarrow \pi^{-}} \cot x$

Answer

$-\infty$

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James Stewart

Biocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$-\infty$

Biocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Heather Z.

Samuel H.

Michael J.

James Stewart

Biocalculus Calculus for the Life Sciences