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

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.