I'm doing calculus while sitting in Shapiro.
I want the limit of lnx times x
as x approaches zero from the right.
So lnx shoots off right out of sight
And thus the limit is infinity times zero.
You know that limits of this form take special action.
They're indeterminate which means caution is key.
If we want to have any hope at all,
then we must turn to using l'Hôpital.
We've got to try to write the limit as a fraction.
Chorus: So we try to reexpress the x
As one divided by x taken to the minus one,
And of course the step that's next
Is combine that with the log to get a fraction, yes.
Then we learn that both terms grow,
By which I mean the bottom oh, and also the numerator.
I guess that's all we need to show:
Now you're just some limit of a ratio.
Now you're just some limit of a ratio.
Now you're just some limit of a ratio.
And now l'Hôpital applies his rule to solve the limit.
He takes derivatives then everything just cancels out.
This process works just fine
For tangent or cosine
And that is all you need to know,
Didn't want you to get caught up on some limit of a ratio!
(Chorus)