limx趋于0,（cos2x)^(1/x^2)=

limx趋于0,（cos2x)^(1/x^2)=

求极限：x→0lim(cos2x)^(1/x²)
x→0lim(cos2x)^(1/x²)=x→0lime^[(lncos2x)/x²]=x→0lime^[(-2sin2x)/(2xcos2x)]
=x→0lime^[-(sin2x)/(xcos2x)]=x→0lime^[-2x/(xcos2x)]=x→0lime^[-2/cos2x]=eֿ²=1/e²