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
What Happened To My $100,000 Remodel
What’s up you guys, it’s Graham here. So I know a lot of you guys have been asking for an update on the status of my now over $100,000 renovation. I guess it’s about time I give everyone an update and discuss what’s going on because it’s been over a month…
Beaker Ball Balance Problem
Here is the set up. I have a balance and two identical beakers, which I fill with exactly the same amount of water, except in one of the beakers there is a submerged ping pong ball tethered to the base of the beaker. And in the other there is an identical…
WHICH PLAYER SHOULD I CHANGE? | Maresca hits back at calls for more Chelsea substitutes
Must proved a very frustrating end to the afternoon for you, and what does it tell you about your Chelsea team? No, yeah, as I said, I just said that probably we did enough to win the game today. Between the first half and second half, I think we created…
Why 70% Of Millennials Are Financially SCREWED
What’s up, Graham? It’s guys here. So, unfortunately, I have some good news and I have some bad news. Now, normally I would ask which one you would want to hear first, but because I’m all alone, just talking to a camera, obviously I’ll just assume that we…
Harpoon Heroes | Wicked Tuna
Right in the front, right down. Look, keep your head down, taking the right side of the pile. Going to come left a little. Still up, just up to the right. 1:00, we’ve got four fish in Hollywood. There are four fish. We’re neck and neck, and we’re hoping f…
Grizzly Bears in Yellowstone, LIVE! | Yellowstone Live
Hi everyone and welcome to West Yellowstone Montana! We are live at the Grizzly & Wolf Discovery Center sponsored by Microsoft Surface. My name is Kelly Barret, and I’m here with Sarah, a naturalist here at the center. Sarah is going to be sharing all…