分别取 x(n) = (2nπ-π/2)^2,y(n) = (2nπ)^2,有 　　　　lim(n→inf.)x(n) = +inf.,lim(n→inf.)y(n) = +inf.,但数列{sin√(x(n))} 与 {sin√(y(n))} 的极限都存在但不相等,据海涅定理知 lim(x→+inf.)sin√x ...