Hello. Hey, we're going expression and were asked to determine the function of, uh, based upon this expression as well as the stuff side number A that we're evaluating at Nebraska calculating woman. So after that, we can have a hint at what our number eight is because we're asked to approach the limit as X goes to 1 may also see it in the denominator that we're gonna be undefined when X equals one. So this told us that our specimen point A is most likely going to be one. Then that brings us to the question What is our potion? And this might be a little tricky because we're looking at it and we're like, Well, that doesn't really look like it's in the form of Ebel's H, uh minus after they. So what? We can dio look at it and try to see if we confected us into two parts and make it a little more sense. But let's evaluate and then return to what we think it could be. So three X squared plus four acts find a Southern can also be written as to factor relation because we have r squared our next to the water and then our constant value, which tells us that it something like plus a or times plus or minus a or something like that. So looking at it, we want a three X even though. And each compartment, because this allows is to get our three x squared when we you are multiplication by part. So what already possible? You know as well we know that we have to have our last part multiply by some factor of seven political seven so really over limited to is something and one because 701 7 So that also told us that one of these is going to be negative story. They're gonna have a negative seven on a positive one or a pilot of seven. Negative, because not feeling a way we can get negative something so we can experience around. But after a little, uh, mixing and matching of these, we see that having seven on the left factory ization is having a negative one on the right. Makes it so that we have are three x squared and then minus three acts plus seven x, which gives us a positive four acts minus seven. So this is equivalent to, um, the same expression to left. And that's how you can do it when you don't really know what you're working with. So if we take this and put it over our X minus one, we see that we have two X minus one. Most canceled. So we're not give in, but women as X approaches one, uh, three X. So when X goes to one, um, this is three times one or seven, which equals Well, that's our limit. But what is our original function? Well, that's gonna be a little trickier, So we know that the derivative can be simplified down to three X plus Southern. So what is the original function? What could the original function be? Well, we can integrate that expression based off of the limit. And that would tell us that perhaps it's three x squared over two plus seven x what I see. But that doesn't really tell us, um, what it could be in terms of, um, having our April's age and our evaluation at a so that's not gonna work. But what could work is looking at this numerator expression and thinking. Well, what happens when we goto one wants. Evaluate, have one. So we have three times one square plus four times one minus. So this is three plus for which goes seven minus seven. Well, that's pretty interesting, because we see that you have a Southern will be evaluated one. And if we're evaluating at one, we have a negative seven in this last part that this tells us that our today is most likely are three x squared. What for Tax? Because if we think about it in terms of, uh, a plus age minus halfway, we have our, um, function of evaluated such that we have, um, there he times one plus h squared, plus four times, one plus age. We can figure that out. But the more important part is what happens when we're evaluating at half of a So we just plug one in. So three times one squared plus four times one. Well, this gives us our of seven. Let's help us that this is pretty good approximation of the potions about all three parts to this. We have the answer to a our first part. So we have a is one. That's our evaluation. What we're evaluating at we have three X squared plus four x, which is our original function. No, we have time, which is our valuation at full of it.