Solution: choose C. This kind of problem is an innovative problem that immediately defines the scene, focusing on in-depth reading comprehension and mathematical literacy. It is not suitable to use traditional solutions. We should firmly grasp the information provided by the stem and the selected branch, analyze and eliminate it, and finally get the answer.

Because the necessary and sufficient condition for the existence of asymptote is that when x tends to infinity, f(x)-g(x) tends to 0;

Therefore, for ①, when x > 1, it does not match, so ① does not exist;

For ②, there is an asymptote, because when x > 1, f(x)-g(x) tends to 0;

For ③, f (x)-g (x) =11/lnx, let p(x)=x-lnx, the second derivative of p(x) r = 1/x2 > 0, lnx < x,.

④ When x tends to 0, f (x)-g (x) = [-2/(1+1/x)+2+1/e] tends to 0, so there is an asymptote.

Therefore, if there is an asymptote, choose 24C.