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.

US Government and Civics Introduction

Battle Over Bathrooms | Gender Revolution With Katie Couric (Bonus Scene)

View All

Flying the Piaggio at 41,000 Feet (Max Altitude!)

Hello from beautiful Jackson Hall, Wyoming, one of my all-time favorite airports to fly out of. We’re back in the Piaggio; you guys have been asking for more content with this thing, so here we are. Today, we’re going to push this airplane to its limits, …

Second partial derivative test intuition

Hey everyone! So, in the last video, I introduced this thing called the second partial derivative test. If you have some kind of multi-variable function, or really just a two-variable function, is what this applies to—something that’s f of X, Y—and it out…

Dad Reacts To My Frugal Lifestyle

What’s up you guys? It’s Graham here! So, I thought I would do something entirely different today and bring my dad on the channel. He’s the one you’ve seen reacting to my Tesla Model 3 and also to a Tesla Model X going 0 to 60 in 2.6 seconds. He’s the one…

The Threat of AI Weapons

I’ll explain more at the end, but let me set up this clip in five words: robot killers, Stephen Fry, watch. Autonomous weapons have been described as the third revolution in warfare after gunpowder and nuclear bombs. They could mount rapid devastating at…

How to Fix a Leaky Wooden Boat | Primal Survivor

NARRATOR: The boats may look simple, but their design is intricate and complex. Ta’u boatbuilders journey deep into the forest– [non-english speech] –to find the 11 different species of tree needed to make a [non-english]. Centuries of experience go into …

Is Meat Really that Bad?

Food is arguably the best thing about being alive. No other bodily pleasure is enjoyed multiple times every day and never gets old. It’s an expression of culture, our parents’ love, and a means of celebration or comfort. That’s why it hits a special nerve…

Graphical limit where function undefined

More Articles