lim -> infinite (3x+4)/(ln(4+4e^x))
lim -> 0 (2/x^4)-(5/x^2)
lim -> infinite (1+(10/x))^(x/4)
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