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.

SpaceX-PLOSIONS: Why It Matters - Smarter Every Day 138

How to learn Japanese in the easiest ways - Japanese learning tips from a native polyglot 🇯🇵

View All

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…

Writing arithmetic series in sigma notation

What I want to do in this video is get some practice writing Series in Sigma notation, and I have a series in front of us right over here. We have seven plus nine plus eleven, and we keep on adding all the way up to four hundred five. So first, let’s jus…

Current State of the Oceans | Sea of Hope: America's Underwater Treasures

People today should really understand that the ocean underpins everything that people care about. If you like to breathe, you’ll listen up because most of the oxygen in the atmosphere is generated out there in the ocean. The ocean shapes temperature, clim…

The Unintended Consequences of Playing God

Imagine you’re going blind. The world slowly becomes a blur. You can no longer see your family or your friends. You can’t see the beauty of a mountain landscape or the ripples in the ocean. Then a YouTuber comes around, offering to give you the gift of si…

Enthalpy and phase changes | Thermodynamics | AP Chemistry | Khan Academy

[Instructor] Let’s say that we have some solid water or ice, and we want to melt the ice and turn the solid water into liquid water. This phase change of solid water to liquid water is called melting, and it takes positive 6.01 kilojoules per one mole to …

Lipstick | Ingredients With George Zaidan (Episode 2)

What’s in here? What’s it do? And can I make it from scratch? It’s the stuff inside yourself. Ingredients. You can think of lipstick as a slightly more complicated crayon. Crayons are made of waxes and colors, and lipsticks have waxes and colors in them t…

Graphical limit where function undefined

More Articles