y=(cosx)^(x^(-2)) とおくと、log(y)=log(cos(x))/x^2、lim[x→0] log(cos(x))/x^2=(0/0) より、
ろぴたるから、lim[x→0] log(cos(x))/x^2=-(1/2)lim[x→0] {sin(x)/x}*(1/cos(x))=-1/2
lim[x→0] y=e^(-1/2)=1/√e