1. The problem statement, all variables and given/known data show for m element of Natural numbers lim b->oo b^m/(e^(sb)) = 0 2. Relevant equations 3. The attempt at a solution Here is what I've started with so far but have ended up at a dead end. I just would like some help to point me in the right direction if possible. Thank you in advance as b->oo b^m/(e^(sb)) yields the indeterminate form oo/oo. both b^m and e^(sb) are differentiable near the limit the derivative of the denominator is non zero so l'hopitals rule is applicable However, when I apply lhopital's rule I get lim b->oo mb^(m-1)/(se^(sb)) My approach was to prove this inductively, ie for m=1 and go from there but I can't even show this is true for m=1. Maybe this is completely the wrong approach. I have convinced myself that I am heading in the wrong direction. Thank you.