Q#3xz2 f(x,z) = x2 + 24Does lim(x,z)-(0,0) f (x,2) exist? Find the limit if it exist:...

Use numerical or graphical means to find the limit, if it exists. If the limit of f as x approaches c does exist, answer this question: Is it equal to $f(c) ?$ $$\lim _{x \rightarrow-2} \frac{x^{2}+3 x+2}{x^{2}-x-6}$$

In this problem where they're asking us to find a left side limit of a function F of X when X is approaching three from the left side. So given that it's a piecewise function, we only need to consider when X is less than three. So when X is less than three, or in this case less than or equal to three F of X is defined by X plus two. Over to easy. They tell us that now they want to see excellent, approaching three from the left hand side so we can try plugging in and see if that works for us. So we're going to get F of X is gonna equal three plus two over to that's going to equal 5/2. That's actually just going to give us her answer. Now, the reason we can plug in is because this original function is continuous, at least on the left side. So we know that we can just plug in and we get our answer, thank you.

Okay for this problem. They want us to find the limit as X approaches. Negative. Two of the function two X over X plus King Cube. Okay, we're gonna have to do this graphically. It looks like there is in vertical aspecto negative too. Okay, so that's a little problematic for eliminating what we're going to have. Ah, something like this. I mean, depict the graph we have Are you quitting in playing here? And it looks like negative, too. We have this vertical ask window, okay to the left or right of it Already going up or down? Well, for slightly to the right of negative, too, than this bottom of our The denominator is going to be negative one point and then ending named, plus two. So this is going to be like a positive number. Really, really small, positive number and on the top will have, like, let's see, negative 1.9 and nine times to just a negative number. But a negative over a really small positive will give us a really huge negative number. So, actually, as we approach from the right, we're going to be approaching negative infinity. And as we approach from the left. Well, different scenarios. Gonna correct. We're still gonna have a negative on top. But on the bottom are gonna have that negative, really small number because it's 2.0. There, there, there, one negative plus two. And then we're gonna cubit it retains the negative was gonna cancel out with a negative on top. So we're actually gonna be approaching positive infinity from the left. So we're going way up here from this direction, But way down here in this direction. So it's already a problem that we were approaching infinity, but we're approaching two different infinities, so keep that in mind when you notice that the limit doesn't exist, okay?

Hi Today we will be solving for the derivative off at F F. Ax equals X squared plus three x using the limit definition off a derivative. The limit definition of a deer a minute was given over here as he limit off age approaching zero off half of Expos age minus affects all over H. Now we can apply this definition using this given function to find the derivative off FX. So let's do that right here. So let's start by assault by writing out the limit of H approaching zero for half of Expos age. Let's start by writing out half of exports age, and we would do this by replacing every ex turn in effects with simply X plus h. So we would do this by writing instead of X squared, right X plus h squared. And instead ofthe three X, we would write three times explosive change. Now he would subtract effects as given in our limit definition, and he would simply copy it down half effects Over here. Linus X squared plus three x. It's helpful to keep the function in parentheses over here to make sure that you distribute your negatives correctly and you would divide this entire thing by H. And we can simplify this further by multiplying out the factors over here and express age and simplifying the entire queen So he could do that by writing. Lim has h approaches hero. Remember to keep it in limine notation while you're simplifying this part So he would simplify express H squared in two X squared plus two ex age plus h squared. And if you don't know how to expand factor factors like this is something that's worth checking out again or reviewing Now we would distribute the three into expose h so he would write plus three x plus three h And now we would distribute the negative into X squared plus three x so he would get minus X squared minus three x oh, over a tch. Now, if you look here, you'LL see that some of our terms he cancelled out, for example, we have positive x were here and negative X squared over here X squared minus X squared is just zero so we can cancel these terms out and we also have positive three ex air here and negative three x over here three x minus three X is just zero so we can cancel that out because say factor each other out. So now we're left with he Lim off h approaching zero uh, to x age plus h squared plus three teenage oh, over a tch. Now notice again that there is an ancient every term in the numerator and only in age in the deep then on later, so we can cancel it out and factor at the age like so. And then we're left with the limit off H approaching zero oh to X plus age plus three. And now, at this point, because we've simplified this enormous equation over here into the small equation here, we can finally find the limit as h approaches zero. This valley here for h will equal zero two x will not change as age is approaching zero and three will not change us. H approaches zero so we can solve for a limit and set the limit as age approaches. Zero off. Two x plus eight plus three is to x plus zero plus three course simply two x plus three. And there you have it. That is your derivative for effects equals X squared plus three x using the limit definition. Thank you for watching

Hi. This is Jordan from numerator. And today we're going to look at these existence of a limit problems. This woman is determined whether the limit of f of X as X approaches three exists and explain. So the first thing we're going to want to know is that this FX we don't really have an expression of work with this auxiliary information down here is what we're gonna use and this problem's really testing is is that the limit as expert, just three here is actually determined by the value of the limit as executed from the left and is like super inches from the right. So if we look at these two guys, we know that the limit is X approaches. Three fromthe left of of X is equal to one. So that tells us that this exists. And the limit as execute your suit from the right of f of X equals one exists. And since he's both exist and they're both equal to one, we can say that the limit is extra just three overall exists and that the limit is except registry of Quebec's, with one