y is equal to g of x.

What I wanna do is I wanna figure out

the limit of g of x

as x approaches positive six

from values that are less than positive six

or you could say from the left, from the, you could say

the negative direction.

So what is this going to be equal to?

And if you have a sense of it, pause the video

and give a go at it.

Well, to think about this,

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 two, looks like it's a little bit more than one.

G of three, it's a little bit more than that.

G of four, looks like it's a little under two.

G of five, it looks like it's around three.

G of 5.5, looks like it's around five.

G of, let's say 5.75,

looks like it's like nine.

And so, as x gets closer and closer to six

from the left, it looks like the value of our function

becomes unbounded, it's just getting infinitely large.

And so in some context, you might see someone

write that, maybe this is equal to infinity.

But infinity isn't, we're not talking

about a specific number.

If we're talking technically about limits

the way that we've looked at it, what is,

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.

Not exist.

This thing right over here is unbounded.

Now 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 six from the right-hand side,

well, let's see.

We have g of eight is there, go of seven is there,

g of 6.5, looks like it's

a little less than negative three.

G of 6.01, little even closer to negative three.

G of 6.0000001 is very close to negative three.

So it looks like this limit right over here,

at least looking at it graphically,

it looks like when we approach six

from the right, looks like the function

is approaching negative three.

But from the left, it's just unbounded,

so we'll say it doesn't exist.