lim x→¼派 (tanx)∧tan2x 求极限.底数是0.25派.

lim x→¼派 (tanx)∧tan2x 求极限.底数是0.25派.
lim x→¼派 (tanx)∧tan2x 求极限.底数是0.25派.

lim x→¼派 (tanx)∧tan2x 求极限.底数是0.25派.
lim(tanx)^tan2x
=lim(1+tanx-1)^tan2x
=lim(1+tanx-1)^[1/(tanx-1)][(tanx-1)tan2x]
底数：lim(1+tanx-1)^[1/(tanx-1)]=e
指数：lim[(tanx-1)tan2x]=lim[(sinx/cosx-1)sin2x/cos2x]
=lim[(sinx-cosx)2sinx/cos2x] 下面利用：cos2x=cos²x-sin²x
=lim[-2sinx/(sinx+cosx)]
=-1
答案e^(-1)

e;利用求对数换成除法指数部分,方法对

sin2x=1;

极限=e^-1=e^-1