limits

[verbal hearth]

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[next wren]

That's a weird way to write it. Why didn't they just write $\lim_{x \to 0^+}$?

[vagrant grove]

Techie Literate

[full rapids]

idk 😭

[next wren]

So what happens if we try direct substitution?

[full rapids]

indeterminate form

[next wren]

Which one?

[full rapids]

0^inf

and inf^zero

[next wren]

Right. So how do we solve that kind of indeterminate form?

[full rapids]

i will not do l hopitals here

[next wren]

...why not?

[full rapids]

its gonna get huge

we have 2-3 minutes for each question

i have an idea

[next wren]

...yes. That is the one correct way.

[full rapids]

first one becomes zero

e^-inf

[next wren]

Right.

[full rapids]

and second one becomes one?

e^0

[next wren]

Prove it.

[next wren]

What's "-ve"?

[full rapids]

like

when x approaches 0+

[next wren]

No.

What does "-ve" mean?

[full rapids]

lnx approaches 0^-

[next wren]

...no it doesn't. It approaches -infinity.

[full rapids]

NONO

huh

how

ouhh

yeee-

it became indeterminate again

[next wren]

What form?

[full rapids]

0*inf

[next wren]

...so then how do we solve that?

[full rapids]

l hopitals this time?

[next wren]

Yes, but first we need to get it into 0/0 or inf/inf.

[full rapids]

how do we do that

[next wren]

Well, we have 0 * inf. And we know 1/inf = 0 and 1/0 = inf (in a limit context).

[full rapids]

how does this help here

[next wren]

...because... we have 0 * inf. So... that's equal to 0/(1/inf) = 0/0 or inf/(1/0) = inf/inf. Like, this is how you do this indeterminate form, always.

[full rapids]

OUUUUU

so its already in this form

can i apply l hopitals?

[next wren]

...if... you transform it into one of those forms... which is the entire point of doing so...

[steady night]

could u not make then both exponentials and have a quotent of a ln and another function in the power then evaluate both limits using lhpitals

i got 2 😭🙏

[full rapids]

Its 1