Name: Limits of combined functions | Limits and continuity | AP Calculus AB | Khan Academy
Uploaded: 2022-07-01T04:32:45.000Z
Duration: 4 min 9 s
Description: 組合功能的限制 |限制和連續性 | AP微積分AB |可汗學院Learn the English Usage: limit,approaching,approach,negative,equal,continuous,defined,exist,divide,plot,exists,sense,graphical,clearer,continuity,instructor,graph,point,combined,calculus,khan...

- [Instructor] Let's find the limit of f of x

of the graphs y equals f of x and y equals h of x.

that this is going to be the same thing as the limit

And let's think about what each of these are.

So let's first think about f of x right over here.

notice the function itself isn't defined there.

But we see when we approach from the left,

the function seems to be approaching the value

And as we approach from the right, the function seems

to be approaching the value of negative one.

As we approach from the right, the value of the function

the function is defined at x equals zero.

We can see that, as we approach it from the left,

As we approach from the right, we're approaching one.

As we approach x equals zero from the left, we approach,

As we approach x equals zero from the right,

And it makes sense that the function is defined there,

is equal to the value of the function at that point

So we have the limit as x approaches zero of h of x

So once again, using our limit properties,

this is going to be the same thing as the limit of h of x

Now what's the limit of h of x as x approaches zero?

as we approach x equals zero from the left,

our function seems to be approaching four.

And as we approach x equals zero from the right,

That makes sense because this is a continuous function.

So the limit as we approach x equals zero should be the same

as the value of the function at x equals zero.

Now let's think about the limit of g of x as x equals,

So from the left, it looks like, as x approaches zero,

the value of the function is approaching zero.

the value of the function is also approaching zero,

And that makes sense that the limit and the actual value

of the function at that point is the same

We have to take four and divide it by zero.

'cause we can't take four and divide it by zero.

So even though the limit of h of x is x equals,

and the limit of g of x as x approaches zero exists,

so this whole entire limit does not exist,

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Limits of combined functions | Limits and continuity | AP Calculus AB | Khan Academy

entire

approach

situation

negative