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.

Warren Buffett's Most Iconic Lecture EVER (MUST WATCH)

Phil Libin at Startup School 2013

View All

Curvature intuition

Hello everyone. So what I’d like to do here is talk about curvature. I’ve drawn on the xy plane here a certain curve. So this is our x-axis, this is our y-axis, this is a curve running through space, and I’d like you to imagine that this is a road of some…

When Life Disappoints You, Don’t Disappoint Life

For many, the disappointments of life justify destructive behaviors towards oneself and others. Entitlement to what they feel they deserve, or what others have and they have not, leads to disappointment if reality doesn’t provide them with what they expec…

RC step response 2 of 3 solve

In the last video on step response, we set up the differential equation that describes our circuit, and we found that it was a non-homogeneous equation. Now we’re going to follow through on the strategy of solving it with a forced response plus a natural …

Three things to know about stocks

When you own a stock, you’re owning a fractional share of a company. Now, there’s three things that I always like to keep people wary of when they buy a stock. The first is, is there’s sometimes a perception that the stock prices everything, that maybe a …

Dark Web: The Unseen Side of The Internet

The Internet has changed everything, from the way we work to the way we play to the way we live. It seems that there’s a corner of the internet for everyone; despite what interests you have, despite what your beliefs are, there’s someone or something out …

Philosophy On Falling In Love

…bring suffering. If it’s merely a passing attachment, it can lead to more pain than joy.” He emphasizes that true love is unconditional and does not depend on the other person meeting our desires. Instead, it’s about caring deeply for another’s well-bein…

Graphical limit where function undefined

More Articles