取xk= π 2 +2kπ,k∈N,显然 lim k→∞ f(xk)= lim k→∞ ( π 2 +2kπ)=+∞,答案A和D排除.取xk=2kπ,k∈N, lim k→∞ f(xk)=0,选项B排除.故选 C