4: In the numerator and denominator there is a difference of infinities. If you wanted to use the l'Hospital rule, you would have to first show that the numerator and the denominator go to infinity. This is true, but how would one prove it? It is an expression where one can use dominance (see the appropriate box), so the denominator can be handled by factoring out the dominant term. However, the same procedure can be used to find the limit of the whole ratio, so you can do it right away.