What if L'hospital's rule doesn't work?
1 Answer
l'Hopital's Rule occationally fails by falling into a never ending cycle. Let us look at the following limit.
by l'Hopital's Rule (
by l'Hopital's Rule (
As you can see, the limit came back to the original limit after applying l'Hopital's Rule twice, which means that it will never yield a conclusion. So, we just need to try another approach.
by including the denominator under the square-root,
by simplifying the expression inside the square-root,
So, we could come up with the limit without using l'Hopital's Rule.
I hope that this was helpful.