Come on...you don't need L'hopitals for any of these. Just think about this

As x gets incredibely huge

So

So

For the secone one combining the fractions give now when you put 0 in there it should be pretty obvious what the answer is

For the third one Im sure you know that

Well in your limit if we let we have that

Now we can see that this is equivalent to

On the inner integral letting again we get