Name: Undefined limits by direct substitution | Limits and continuity | AP Calculus AB | Khan Academy
Uploaded: 2022-07-02T02:59:08.000Z
Duration: 2 min 14 s
Description: 直接替換的未定義限制 |限制和連續性 | AP微積分AB |可汗學院Learn the English Usage: limit,log,continuous,natural,evaluate,defined,evaluated,equal,exist,magenta,substitution,figure,numerator,denominator,continuity,graph,pause,calculus,khan...

Modal verbs - A2

- [Voiceover] Let's see if we can figure out the limit

of x over natural log of x as x approaches one.

Adverbs of frequency

And like always pause this video and see if you can

Well we know from out limit properties this is going to

Now this top limit, the one I have in magenta,

it's defined for all real numbers and it's continuous

So it's continuous to limit as x approaches one of x.

It's just gonna be this evaluated x equals one.

For the numerator here we just evaluate to a one.

natural log of x is not defined for all x's,

therefore it isn't continuous everywhere.

And since it is continuous at x equals one,

then the limit here is just gonna be the natural log

So this is just going to be the natural log

It is was zero over zero, we wouldn't necessarily be

as we will learn in the future there are tools we can apply

when we're trying to find limits and we evaluate it

Subtitles ListPlay Video

Undefined limits by direct substitution | Limits and continuity | AP Calculus AB | Khan Academy

figure

straight

necessarily

bit