1. The problem statement, all variables and given/known data If |x| is large, then f(x)=(x5-x4+x3+x)/(x3-1) is approximately what? 2. Relevant equations Just use long division 3. The attempt at a solution Well, I just started out dividing the polys, and I ended up with f(x)=x2-x+1 + (x2+1)/(x3-1) I thought, well, if x is very large, then the fraction at the end there will begin disapearing and tend towards 0. The solution in the book agreed, but I'm confused about something. The solution in the book says "as the limit as x --> infinity, (x2+1)/(x3-1) = 0, so f(x) ≈x2-x+1 But this doesn't make sense because as x tends to infinity, x2-x+1 will blow up towards infinity. I guess I am just not wrapping my mind around how f(x) is approximately x2-x+1 for |x| "very large". Is it just because the fraction goes to 0 faster than x2-x+1 goes to infinity?