Graphical limit where function undefined

2m read

·Nov 11, 2024

So we have the graph of ( y = f(x) ) right over here. What we want to do is figure out the limit of ( f(x) ) as ( x ) approaches -4. So, what does that mean?

Well, a limit is saying, “What is my function approaching as the input of that function approaches, in this case, -4?” As the input approaches a value, and as we see in this example, the function doesn't necessarily have to be even defined at that value. We can see ( f(4) ), you go to ( x ) at -4, and you see that ( f(4) ) is undefined. So this is not defined, but as we'll see, even though the function isn't defined there, the limit might be defined there.

Actually, it could go the other way around; sometimes a function is defined there, but the limit is not, and we'll see that in future videos. But let's just get an understanding here of what's going on as ( x ) approaches -4 from values greater than -4 and from values less than -4.

Well, let's first think about values greater than -4. So when ( x ) is -1, this is ( f(-1) ). This is ( f(-2) ). This is ( f(-3) ). This is ( f(-3.5) ). This is ( f(-3.9) ). This is ( f(-3.99) ). This is ( f(-4.0001) ). You can see the value of our function, as ( x ) gets closer and closer to -4 from values greater than -4, seems to be approaching 6.

Let’s see if that's true from the other direction, some from values less than -4. So this is ( f(-7) ). This is ( f(-5) ). This is ( f(-4.5) ). This is ( f(-4.1) ). This is ( f(-4.01) ). It looks like it's getting awfully close to a little bit more than 6. So it seems, as we get closer and closer to -4, the value of our function is approaching positive 6.

15 Invisible Assets to Your Personal Economics

Citing evidence in literary analysis | Reading | Khan Academy

View All

Mr. Freeman, part 00

So here you are. You’ve laid your fears and doubts on the bonfire for me to burn the hell out of them. Now I step out into the center of this effin coliseum with a torch and a gas can in my hands. In front of me — a crowd of naked people backing up agains…

5 Ways to Forgive Someone Who Wronged You

Feelings of bitterness and revenge are like heavy stones we carry around on our backs. And if we’re unable or unwilling to throw these stones onto the ground and walk away from them, we’ll not only exhaust ourselves; the load also increases because of new…

I’ve Read 50 Business Books—These Are The 3 You MUST READ

[Music] In the last 12 months, I made 113k 851 outside of YouTube sponsorships and AD Revenue, all without having any full-time employees for a long time. Even though I don’t want to admit it, I relied heavily on AdSense and sponsorships. While they worke…

Derivatives of tan(x) and cot(x) | Derivative rules | AP Calculus AB | Khan Academy

We already know the derivatives of sine and cosine. We know that the derivative with respect to x of sine of x is equal to cosine of x. We know that the derivative with respect to x of cosine of x is equal to negative sine of x. So, what we want to do in…

Identifying the constant of proportionality from equation | 7th grade | Khan Academy

When you hear “constant of proportionality,” it can seem a little bit intimidating at first. It seems very technical, but as we’ll see, it’s a fairly intuitive concept, and we’ll do several examples. Hopefully, you’ll get a lot more comfortable with it. …

More uses for commas | Punctuation | Grammar | Khan Academy

Hello Garian, and hello Paige. Hi David, Paige. I have a question for you. What’s up? You like cheese, don’t you? Well, yes, I do. So Paige, what I’ve just asked you is an example of what’s called a tag question. So I’m making an assertion, and then I’m …

Graphical limit where function undefined

More Articles