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RaulQuestion 50.6/1ptsNumerically estimate lim I? table below:16 to onc decimal place by flling the numericalMake sure to enter the answers with number of digits ...

Question

RaulQuestion 50.6/1ptsNumerically estimate lim I? table below:16 to onc decimal place by flling the numericalMake sure to enter the answers with number of digits according to the conventions stated in lecture:~161.929.6791.9931.760899931,9761.999931.99769999931.99981,99999931.99991' _ 16 In conclusion; we can say the limit is lim 373 T - 2

Raul Question 5 0.6/1pts Numerically estimate lim I? table below: 16 to onc decimal place by flling the numerical Make sure to enter the answers with number of digits according to the conventions stated in lecture: ~16 1.9 29.679 1.99 31.7608 999 31,976 1.9999 31.9976 99999 31.9998 1,999999 31.9999 1' _ 16 In conclusion; we can say the limit is lim 373 T - 2



Answers

Use the table of values to estimate $\lim _{x \rightarrow 1} f(x)$
$$
\begin{array}{|c|cccccccc}{x} & {0.9} & {0.99} & {0.999} & {0.9999} & {1.0001} & {1.001} & {1.01} & {1.1} \\ \hline f(x) & {3.9} & {3.99} & {3.999} & {3.9999} & {4.0001} & {4.001} & {4.01} & {4.1}\end{array}
$$

So in this question, we want to use the table of values toe, help us evaluate the limit as X goes toe one of f of X and, ah, What that means is we want to take a look at the X values that approach one and see what their Y values turn into. So as we move toward 0.9999 and one point there is there, is there one? We see that the Y values or F of X values are getting closer to four, and that is Thea answer to the problem.

Everybody we're doing Chapter two, Section three Problem 20. The goal of this is to be able to find out what the limit as extra purchase. Negative one is as you come from both sides and they give you a whole bunch of points and they want you to plug those points in and then get kind of a feel for what you think that the limit is approaching. So if you actually plug in a negative one, you'll get undefined. The reason for that is because if you take the graph right and you solve it, you'll find that this is, you know, pretty eliminating X over. Ah, you know, this is the top civil fight, and then you take the bottom in your simple client tear and you get X minus two and you get X plus one that this is the culprit for breaking. There's the whole at make it too, so that will fall apart, and then you get X over X plus one. So this is the function that we're actually dealing with. The reason that we're talking about a limit and not an actual point evaluation is because if you plug in negative one you'll divide by zero. You'll get negative one over zero. Get something that is undefined, which means you'll have you'll have an error at that point. So the goal at hand is to be able to find out. Okay, Well, what is the point? What is it? What is it? Actually, and so the way to find out that in a pretty remedial way, is just to plug in a bunch of stuff that's around negative one plug in a bunch of stuff that's from the left and come to the right plugging a bunch of stuff that's from the right and go to the left and then kind of see what it it feels like. So they give you, give you points to pull again, right? If you plug in zero, you get zero if you plug in, Um, you know, so So we'll hit it from this. Right here is negative one, right? We don't know what it is. We have a slew of things like that. We have a slew of things that we could put it over here. We have a slew of things that will be over there. Those will be things that are bigger and those would be things that are smaller than negative one. So, for example, they have you plug in, like negative negative 0.5, right? That's that's a little bit bigger and negative. 0.5 you get ah, you know, negative 0.33 repeating negative 1/3. So if you do that, you'll end up finding, you know that it's like you don't really have a good idea of what it is yet, But if you plug in, you know, negative 0.9, which is pretty close to negative one, you'd say, Um, you get negative point a one a, you know, and then some other stuff. But the number got smaller, so that's a limiting. It's not getting bigger, it's getting smaller. So you got smaller and so we should probably see you know what happens Then They give you numbers, you know, like like inner negative 0.999 Really, really, really small. And you end up getting negative. 0.9 nine, you know, like eight something. So we went from native 3rd 2 Negative 20.8182 negative 9.9 98. For me, the distance that it creates this increased by 980.5 between these about this only increased my 0.1, and there was a pretty, you know, small jump here. But my intuition is telling me that this thing jumps and then jumped by a smaller amount. It feels like it's not gonna jump anymore. Like my intuition for this. I would guess that the limit of it is negative point, but I don't know the way to check again. It's too mean plugging some stuff on the left side, right so you can plug in like if you put in negative to, um, the original thing would have given you a hole, so that's not super helpful. So we'll put a gun to get, too, because I was just be undefined. But if you're playing like a negative 1.5 right, which is something that's bigger, well, smaller, I mean, it's always confusing. Things get negative but smaller in the sense that it's more to the left right? So if you minus 0.5 ah, if you plug that into getting to give three, so that sort of pushes us away from negative one right? But let's get it closer to negative one, right? Let's do Ah negative 1.1. Did you book a negative 1.1? You get negative one point, you know, to repeating. Well, that jumped quite a lot, right? And then if you do, you know, like another one of the examples they have is negative. 1.1 that's really, really close. The negative one. That'll give you a really good idea of what it is. And then in the giving you, you know, negative one point. Oh, too. That's very close to negative one. This pushes me to think that it would actually be negative one. And that's why if I plugged in the values on the right here, they seem to be pushing for negative one eye pulling in these values on the left. They also seem to be pushing for negative one. After all this work, I would be able to definitively say that it feels like the limit of this function as X approaches. Negative one from both sides is negative. One hope this help until next time

So we're gonna be guessing this limit using these values. What you're gonna do is take all of these X values and plug them in for X, and then you might want to write them in a list. And you might want to divide it right here because all of these values on the left are approaching negative one from one side, and these values on the right are approaching negative one from the other side. So what I'm gonna do is write the's going top to bottom. So first all plugging zero per acts and write the answer here. The negative 00.5 negative 0.9 and so on. So if we pulled in zero gets here, Hope you plug in naked of 00.5, you get a negative one, then negative nine. Negative. 19 negative 99 negative. 999. And with these points we get to Bree 1100 wine and 1000 in line. So what is the limit as X approaches negative one. Well, as we get closer to negative wine with these values over here on the left, it looks like it's approaching negative. 1000. We go with these values over here on the right, it looks like it's approaching some positive number, so this means that the limit does not exist.

For the given problem, we want to guess the value of the limit if it exists, Knowing that we have the limit as X approaches -1 of the same function as the previous problem, so that X is approaching a negative one. We're going to consider -0.9, repeating. So this is going to be approaching from the right, Okay. And we see that this is going to negative infinity. Um and then we see that if we approach from the right, So a negative one point approach from the left, so negative 1.2 or one, we keep increasing as we see this is going to positive infinity. So we see that because of this, the limit will not exist. We can also confirm this with the graph. As we approach from the right, we go to negative infinity. As we approach from the left, we go to positive infinity. So the limited self. The limit itself will not exist.


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