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Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).$\lim _{x \rightarrow 2^{-}} \frac{x^{2}-2 x}{x^{2}-4 x+4}$

$-\infty$

Calculus 1 / AB

Chapter 2

Limits

Section 3

Limits of Functions at Finite Numbers

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

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