yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

One-sided limits from graphs: asymptote | Limits and continuity | AP Calculus AB | Khan Academy


2m read
·Nov 11, 2024

So over here we have the graph of y is equal to G of x. What I want to do is figure out the limit of G of x as x approaches positive 6 from values that are less than positive 6, or you could say from the left, from the negative direction. So what is this going to be equal to? If you have a sense of it, pause the video and give a go at it.

Well, to think about this, let's just approach, let's just take different x values that approach six from the left and look at what the values of the function are.

So G of 2 looks like it's a little bit more than 1. G of 3, it's a little bit more than that. G of 4 looks like it's a little under 2. G of 5, it looks like it's around 3. G of 5.5 looks like it's around 5. G of, let's say, 5.75 looks like it's like 9.

As x gets closer and closer to 6 from the left, it looks like the value of our function just becomes unbounded. It's just getting infinitely large. In some contexts, you might see someone write that maybe this is equal to infinity, but infinity isn't a specific number.

If we're talking technically about limits the way that we've looked at it, you'll sometimes see this in some classes, but in this context, especially on the exercises on Khan Academy, we'll say that this does not exist.

This thing right over here is unbounded, and this is interesting because the left-handed limit here doesn't exist, but the right-handed limit does. If I were to say the limit of G of x as x approaches 6 from the right-hand side, well, let's see.

We have G of 8, is there. G of 5 is there. G of 6.5 looks like it's a little less than -3. G of 6.01, a little even closer to -3. G of 60000000000, it's very close to -3.

So it looks like this limit right over here, at least looking at it graphically, looks like when we approach 6 from the right, the function is approaching -3. But from the left, it's just unbounded. So we'll say it doesn't exist.

More Articles

View All
Decomposing angles | Math | 4th grade | Khan Academy
What is the measure of angle EAC? So, we have this symbol here which means angle and then these three letters: E, A, C. Now, to measure angle EAC, we need to first find angle EAC down here on our picture. The way we can do that is use these three letter…
My Investing Plan For 2023 (How To Prepare)
What’s up, Graham? It’s guys here. So 2023 is probably going to be one of the most confusing years for investing. After all, stocks are the cheapest they’ve been in two years, but there’s a chance they could drop even further. Real estate has only starte…
How Do You Get a Haircut in Antarctica?: Day in the Life of a Scientist | Continent 7: Antarctica
[Music] So this is my Scott based haircut. This is a new one for me. I can say I’ve got my haircut in Antarctica by a butcher. By butcher, that’s a carpenter, and he’s only got one eye, and he’s half L, and he’s only got one eye. He says, “Half fine, here…
A Tale of Two Atoms | Cosmos: Possible Worlds
The writer H.G. Wells, who first imagined time machines and alien invasions, had a nightmare of a future world where atoms were weaponized. In his book called “The World Set Free”, written in 1913, he coined the phrase atomic bombs and loosed them on help…
Family living in the wild builds a sail to cross the bay | Home in the Wild
(Hudson cooing) TORI: Wesley’s being so quiet. JIM: I know. He’s being so good. TORI: If the kids aren’t crying, things are good. JIM: Yeah. We got a tailwind. It’s a paddler’s dream. TORI: Yeah, just my concern is just the wind past this point, basi…
World's Heaviest Weight
An apple weighs about 1 newton; the world record for jet engine thrust is 570,000 newtons. And the Saturn V rocket that launched people to the moon had a thrust of 33,360,000 newtons. But how can we measure forces this big accurately? Well, we need to ask…