In class, we sketched out the fact that polynomial functions grow slower than exponential functions, which includes statements like n100O(en). Our method was using l'Hopital's rule "several times," but mathematically speaking, the "several times" part is informal and should instead be written in terms of a proof by induction. Give a formal proof, using induction, that limxexxi=0 for all integers i0. (Hint: the base case is i=0 instead of 1 , and for the inductive step, you should be applying l'Hopital's rule exactly one time.)