There are two kinds of asymptotic behaviour in which we are generally interested: behaviour as [math]x\longrightarrow\infty[/math], and behaviour around points [math]x_0[/math] such that [math]\lim_{x\longrightarrow x_0}f\left(x\right)=\pm\infty[/math]. Rational functions are a good example to study to get the idea of asymptotic analysis as we can use partial fractions to separate out these different behaviours.