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.

The BENEFITS of IGNORING People | STOICISM

The Perils of Downhill Cycling | Science of Stupid: Ridiculous Fails

View All

Eyes on Orcas | Continent 7: Antarctica

[music playing] [splash] [shout] NARRATOR: After a season of frustration– BEN SHARP: Right there. NARRATOR: –Regina and her team have a killer whale in sight. BEN SHARP: He’s coming towards the edge. NARRATOR: Now, they just need it to be in range. …

How price controls reallocate surplus | APⓇ Microeconomics | Khan Academy

What we’re going to talk about in this video is the effect of price controls on changing how the surplus, the total surplus, is reallocated between consumers and producers. We already touched on this in other videos, the video on rent control, the video o…

Woodpeckers Defend Their Food Supply | National Geographic

[music playing] NARRATOR: Day breaks over the lovely forested south rim of the canyon, lighting up a dead pine that would seem to have little purpose. But this pine is the central bank and trust of the acorn woodpecker. And every inch is studded with nea…

Lagrange multiplier example, part 1

So let’s say you’re running some kind of company, and you guys produce widgets. You produce some little trinket that people enjoy buying. The main costs that you have are labor—you know, the workers that you have creating these—and steel. Let’s just say …

Hummingbird Aerodynamics- High Speed Video - Smarter Every Day 27

Hey, it’s me, Destin. So to fly slow is one of the more difficult things to do because you don’t have as much airflow over your control surfaces. To fly at zero air velocity is the hardest thing to do of all. Over the past weekend, I’ve been making observ…

Before You Visit Angkor Wat, Here's What You Need to Know | National Geographic

Eager to experience a spectacular sunrise at Cambodia’s ancient Angkor Wat? Here’s everything you need to know to get to this iconic site and make the most of your visit. Angkor Wat is actually just one of over a thousand temples that make up the ancient…

Graphical limit where function undefined

More Articles