x→0lim (1+2tanx)^cotx=lim (1+2tanx)^(1/tanx)=lim (1+2tanx)^(2/2tanx)=lim [(1+2tanx)^(1/2tanx)]^2根据复合函数的极限运算：=[lim (1+2tanx)^(1/2tanx)]^2根据重要的极限：lim(x→0) (1+x)^(1/x)=e=e^2有不懂欢...