Name: Estimating limits from tables | Limits and continuity | AP Calculus AB | Khan Academy
Uploaded: 2022-06-30T05:31:10.000Z
Duration: 3 min 24 s
Description: 從表中估計限制 |限制和連續性 | AP微積分AB |可汗學院Learn the English Usage: approaching,reasonable,limit,approach,estimate,greater,inference,graph,sample,roughly,sudden,draw,table,tempting,substitute,continuity,jumping,select,drawing,pause,point,teacher,doesn...

- [Teacher] The function g is defined over the real numbers.

What is a reasonable estimate for the limit

It gives us the x values as we approach five

from values less than five and as we approach five

it even tells us what g of x is at x equals five.

And so, given that, what is a reasonable estimate

Alright now let's work through this together.

So let's think about what g of x seems to be approaching

as x approaches five from values less than five.

Let's see at four is it 3.37, 4.9? It's a little higher.

We're only a thousandth away, we're at 3.68.

it looks like we're kind of jumping to 6.37.

And once again, I'm making an inference here.

But then if we approach five from values greater than five.

At six we're at 3.97; at 5.1 we're at 3.84.

So a thousandth below five and a thousandth above five

would be, well it look like we're approaching 3.68.

When we're approaching from values less than five.

as we approach five from values greater than five.

It doesn't matter that the value of five is 6.37.

a reasonable estimate for the limit would be 3.68.

And this is probably the most tempting distractor here

because if you were to just substitute five;

have to be what the actual function equals at that point.

So an example of this, so if this is five right over here,

At the point five the value of my function

is 6.37, so let's say that this right over here

so that's four, actually let me spread out a little bit.

But as we approach five, so if this, that's 6.37;

So the graph, the graph might look something like this.

We can infer it looks like it's doing something like this.

Where it's approaching 3.68 from values less than five

and values greater than five, but right at five,

I don't know for sure if this is what the graph look like

once again, we're just getting some sample points.

But this would be a reasonable inference.

We are approaching 3.68, even though the value

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Estimating limits from tables | Limits and continuity | AP Calculus AB | Khan Academy

approach

matter

scale

roughly