Yes, the limit is allowed to be infinity. You may see this from the proof, for example in the General Proof section in the corresponding Wikipedia page. You would need some preliminary knowledge in calculus like the mean value theorem, though. The key point is that the expression is squeezed between the infimum and supremum of the derivative quotient, while by assumption both the limsup and liminf are just the limit (of the derivative quotient) at that point. When the limsup and liminf take on (negative) infinity, which they are allow to by definition, the desired limit is bounded above by negative infinity or below by positive infinity. This is in a similar vein as the comparison test: if something is always no less than another thing which blows up to infinity at some point, then it must also blow up to infinity at the same point.
I love Lopitals rule!!
¡Use the Lopital’s Lu!!!!
=)
Thanks for this!!!
Limit 3: Can you really use LH if the limiit becomes (negative) infinity?
Yes, the limit is allowed to be infinity. You may see this from the proof, for example in the General Proof section in the corresponding Wikipedia page. You would need some preliminary knowledge in calculus like the mean value theorem, though.
The key point is that the expression is squeezed between the infimum and supremum of the derivative quotient, while by assumption both the limsup and liminf are just the limit (of the derivative quotient) at that point. When the limsup and liminf take on (negative) infinity, which they are allow to by definition, the desired limit is bounded above by negative infinity or below by positive infinity.
This is in a similar vein as the comparison test: if something is always no less than another thing which blows up to infinity at some point, then it must also blow up to infinity at the same point.
Great video, but let's never forget you can't do that with sin(x)/x when approaching 0!!! Such a common mistake
why?
I will let BPRP from the past explain:
ua-cam.com/video/mZiPdyHyUvE/v-deo.html&ab_channel=blackpenredpen
@@BenDover69831coz its a formula
@@BenDover69831 because the derivative of sine is derived using that identity, so if you use LH it would be circular
@@divisix024 If you define sin(x) using power series you don't have that limitation.
Good old Loppy Doll. ;)
And without l'hopital's rules, can you solve it?! 😀😉
Great video, but I think autocorrect got you. L' HoSpital rule?? I know it's just one letter different, but gave me a little laugh. :)
♥
❤😂😂
After seeing this video I think I'll cancel my reservation in the L'Hospital