Limits and Continuity · Superchallenge problem

For each real $x$ define $f(x)=\displaystyle\lim_{n\to\infty}\dfrac{x^{2n+1}+ax^2+bx+2}{x^{2n}+1}$, where $n$ runs through the positive integers. If $f$ is continuous for all real $x$, find $ab$.