The numerator is a DEFINITE integral,whicb is a number. So technically,only the denominator is a function of t. However,clearly the numerator goes to infinity,so it's not a limit that exists so by that reasoning alone, the limit doesn't exist. In that sense,the problem is really a trick question. You have to recognize that the numerator doesn't exist,which means the limit cannot exist! I made that mistake in my initial attempt to solve the problem-I attempted to use L'Hopital's rule-in essence, I treated the numerator as an indefinite integral Which is course,completely wrong. Which is why it really is critical to be absolutely clear what terms are present! Carelessness can cost!