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.

Writing decimals and fractions from number lines

Her "Classroom" is an Environmental Theme Park | Best Job Ever

View All

Conditions for IVT and EVT: graph | Existence theorems | AP Calculus AB | Khan Academy

So we have the graph of ( y ) is equal to ( h ) of ( x ) right over here and they ask us, does the intermediate value theorem apply to ( h ) over the closed interval from negative one to four? The closed interval from negative one to four right over here…

Free response example: Significance test for a mean | AP Statistics | Khan Academy

Regulations require that product labels on containers of food that are available for sale to the public accurately state the amount of food in those containers. Specifically, if milk containers are labeled to have 128 fluid ounces and the mean number of f…

Limits at infinity of quotients with trig (limit undefined) | AP Calculus AB | Khan Academy

Let’s see if we can figure out what the limit of ( x^2 + 1 ) over ( \sin(x) ) is as ( x ) approaches infinity. So let’s just think about what’s going on in the numerator and then think about what’s going on in the denominator. In the numerator, we have (…

10 People + AI = Billion Dollar Company?

What is the state of these AI programmers? Like, is it reliable yet, and where are we at? Well, we just see software companies have way less employees and converge on a point where you could have unicorns—billion-dollar companies—that have like 10 people …

Why Most People Will Never Be Successful

Most people will never be successful, and it’s got nothing to do with who they are or where they’re born. It’s just that they’re unaware of the things that they themselves are doing that keeps them from success. And today that’s exactly what we’re talking…

Crowd-funding: Tips

So, as some of you might know already, uh, I’ve been running a crowdfunding campaign to fund the production of the follow-up to my George or to help animation that I made last year. It’s in the final days of the campaign, so if you didn’t check it out alr…

Graphical limit where function undefined

More Articles