极限问题limx趋向于0cosx的1⼀sinx次方

2025-02-22 09:11:56
推荐回答(2个)
回答1:

原式=lim[(1-sin^2(x))^(1/sin^2(x))]^(0.5*sinx)
=e^0
=1

回答2:

L = lim(x→0)(cosx))^(1/sinx)
lnL = lim(x→0)ln(cosx))/sinx (0/0)
= lim(x→0)[-sinx/cosx]/cosx
=0
L =e^0 = 1

lim(x→0)(cosx))^(1/sinx) =1