question: what number does converge to?
what I've done: sort of use L'Hopital's rule by taking derivative of numerator and denominator => so wouldn't this diverge?
Your derivatives are also correct, BUT, the numerator and denominator still both tend to .
In fact, you would need to work out the numerator's and denominator's derivatives exactly times to make something not tend to .
After derivatives of the numerator and denominator have been taken, you should have
since the denominator tends to .
Of course, like pomp said, it's easier to just write the fraction as .