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
MAKE YOUR CAT A DJ -- and more! LÜT #18
Bake two pies at the same time and then relax on pancake pillows. It’s episode 18 of LÜT. You can also choose to use emoticon pillows or a True Blood necklace. If you’re a neat freak, protect your tables with Portal 2 warning sign coasters. And then stor…
Creativity break: How do you apply creativity in algebra | Algebra 1 | Khan Academy
[Music] So if you’re trying to communicate a complex topic such as mathematics or a mathematical problem to the general public who might not be familiar with the specifics behind that problem, there are many different ways to help you get that concept acr…
Turning Your Users Into Paying Customers
The best feedback you’re gonna get about your product is in the three seconds after you tell them the price. Yes. [Music] Hello, this is Michael with Harj and Brad. Welcome to Inside the Group Partners Lounge. So, as you see Group Partners, we find ours…
How to find a good deal / off market properties in Real Estate
What’s up, you guys? It’s Graham here. So one of the questions I get asked a lot is how do you find a good deal or how do you find something off-market in real estate. So I’m going to be sharing my thoughts about this. Now, I’ve been buying properties si…
15 Things That Make You WEAKER
Growth begins when we begin to accept our own weakness. Jean Vanier. Do you know there are some things you indulge in that could make you weak? Sometimes those things could be harmful to your health and, of course, lead to unproductivity. Weakness, simpl…
Thanks to Shrimp, These Waters Stay Fresh and Clean | Short Film Showcase
[Music] The first time I saw it, I couldn’t believe it. I mean, it was like the Fawn; it was completely different than anything I’d seen before. When you get eight or ten species all in a small pool still coexisting, and they’re all shrimp or crabs, it’s …