INSTRUCTOR: Welcome. In this video, we're going to evaluate a limit using a table. And I've gone ahead and picked some points for you. And what we're interested in is the limit of this function here as x approaches 1. 

So if I were to sketch out a number line, here's 1. Here's one half, which corresponds to this value right here. And here's 1 and 1/2, which corresponds to this value over here. Now, of course, 0.99-- and I'm estimating kind of where it would be-- is here. And 1.01 is here. 

So what is happening is this orange table-- the one I've labeled in orange, that is-- shows us what happens when we go in this direction, that is, when we approach 1 from the positive direction or from the right. Whereas this table here in blue kind of demonstrates what happens as we approach 1 from this other direction, that is, from the left or from the negative direction. 

And you're probably thinking, oh, Ms. G, one half is a negative. It's not. 0 is here, and negative numbers would follow further left. So this is the negative direction or from the left. So that's where these numbers came from. 

And let me erase a bit. So you're going to want to open up GeoGebra. And I have GeoGebra open. So you're going to input y equals and then a division symbol to get your fraction. In the numerator, you want x minus 1. Then you hit the side arrow to the right to get to the denominator, where you type in x squared minus 1. 

And now let's go ahead and create a table of values by hitting these dot, dot, dots, right here, these dot, dot, dots, table of values. I am going to start at 0.5, I'm going to end at 1.5, and I'm going to use a step of 0.1. That will still leave these two blank. 

OK. So let's write in some numbers. So take a moment and recreate this table. And I want you to make your table from 0.99 all the way to 1.01, and use a step of 0.01. So please pause your video and create that table. 

So you should have what follows here. And I purposely rounded this value here to four decimal places because I really want us to see, this is not exactly one half. 49.75 rounds to 0.5, but it's not exactly one half. 

So what are we looking at here? Well, this function is it approaches 1 as f-- excuse me, as x approaches 1 from either direction, the function f of x is getting very close to one half. That tells us that the limit of x minus 1, this entire quantity, divided by x squared minus 1. So the limit of this as x approaches 1 is equal to one half. I hope this video was helpful.