limx→0(cosx)^(1/x^2)求解
问题描述：
limx→0(cosx)^(1/x^2)求解
lim(x→0)((cosx)^(1/x^2))
答
lim(x→0)((cosx)^(1/x^2))
=lim(x→0)[1-2sin^2(x/2)]^(1/x^2))
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2(x/2)^2)]}^(-1/2)
=lim(x→0){[1-2sin^2(x/2)]^(-1/[2sin)^2(x/2)]}^(-1/2)
=e^(-1/2)