Name: Unbounded limits | Limits and continuity | AP Calculus AB | Khan Academy
Uploaded: 2022-06-30T00:55:01.000Z
Duration: 2 min 32 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Past simple

we have the graph of y is equal to one over x squared.

And my question to you is what is the limit

of one over x squared as x approaches zero?

Pause this video, and see if you can figure that out.

you immediately see something interesting

it just gets larger and larger and larger.

As we get values closer and closer to zero from the right,

So terminology that folks will sometimes use,

where they're both going in the same direction,

but it's unbounded, is they'll say this limit is unbounded.

In some context, you might hear teachers say

and it definitely does not exist if you're thinking about

In future videos, we'll start to introduce ideas of infinity

and notations around limits and infinity,

where we can get a little bit more specific

This right over here, you might recognize

as the graph of y is equal to one over x.

So I'm going to ask you the same question.

what's the limit of one over x as x approaches zero?

All right, so here, when we approach from the left,

we get more and more and more negative values.

While we, when we approach from the right,

we're getting more and more positive values.

where we're not getting unbounded in the same direction,

we were being unbounded in the positive direction.

we're getting unbounded in the negative direction.

While from the right, we're getting unbounded

And so when you're thinking about the limit

as you approach a point, if it's not even approaching

the same value or even the same direction,

you would just clearly say that this limit does not exist,

So this is a situation, where you would not even say

Because you're going in two different directions when you

approach from the right and when you approach from the left,

you would just clearly say does not exist.

Subtitles ListPlay Video

Unbounded limits | Limits and continuity | AP Calculus AB | Khan Academy

specific

approach

scenario

context