Name: Formal definition of limits Part 1: intuition review | AP Calculus AB | Khan Academy
Uploaded: 2022-07-05T14:15:16.000Z
Duration: 3 min 36 s
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The imperative

Let's review our intuition of what a limit even is.

To-infinitive

So let's say this is my y-axis, so try to draw a vertical line.

So let's say this right over here is my x-axis.

So let's say my function looks something like that,

could look like anything, but that seems suitable.

So this is the function y is equal to f of x.

And just for the sake of conceptual understanding,

I'm going to say it's not defined at a point.

You can find the limit as x approaches a point where

but it becomes that much more interesting, at least for me,

or you start to understand why a limit might be relevant

where a function is not defined at some point.

Now, the way that we've thought about a limit

is what does f of x approach as x approaches c?

f of x, for our function that we just drew, is right over here.

That's what f of x is going to be equal. y is equal to f of x.

When x gets a little bit closer, then our f of x

When x gets even closer, maybe really almost

at c, but not quite at c, then our f of x is right over here.

And the way we see it, we see that our f of x

seems to be-- as x gets closer and closer to c

it looks like our f of x is getting closer

and closer to some value right over there.

Maybe I'll draw it with a more solid line.

when x was getting closer to c from the left,

But what happens as we get closer and closer

to c from values of x that are larger than c?

Well, when x is over here, f of x is right over here.

And so that's what f of x is, is right over there.

When x gets a little bit closer to c, our f of x

When x is just very slightly larger than c, then our f of x

And we call that value, that value that f of x

write that mathematically is we would say the limit of f

And this is a fine conceptual understanding of limits,

and you're ready to progress and start thinking

But this isn't a very mathematically-rigorous

And so this sets us up for the intuition.

In the next few videos, we will introduce

of limits that will allow us to do things

like prove that the limit as x approaches c