请数学高手,帮我求这题的极限.谢!

1^∞型极限,可用重要极限lim(x→0) (1+x)^(1/x)=e
lim(x→0) (1+tanx)^(2/x)
=lim(x→0) (1+tanx)^[(1/tanx)*(2tanx/x)]
=[lim(x→0) (1+tanx)^[(1/tanx)]^[lim(x→0)(2tanx/x)]
=e^[lim(x→0)(2tanx/x)]
=e²