I found this in the solutions part of my textbook. Why does this even work? There's no explanation at all.
How is bringing up the derivative of cos here even relevant to finding this limit?
Are you OP?
L'hopital is a method to solve limits which are undetermined (you know, when you evaluate and you get 0/0 and stuff like that)
If you are just learning limits, then I would assume your teacher didn't tell you about this. That's because teachers at first expect you to solve limits without l'hopital, to make sure you learn.
>teachers hates this trick
>learn this easy way to solve limits.
Okay, so assuming yo have an undetermined function. differentiate the numerator and then differentiate the denominator BY SEPARATE. Don't use division rule.
d/dx (x) = 1
d/dx (cos(x)) = -sin (x)
your limit will be lim x->0 -sin(x)/1 = 0
>How is bringing up the derivative of cos here even relevant to finding this limit?
What do you mean "how is it relevant"?
He recognized that the limit equals the derivative and it enables him to compute the value he wants to compute.
Say he wouldn't "bring up the derivative here". Well then he'd have to argue somehow else what the limit is.