# 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.