lim{[1+f(x)]^[1/g(x)]},f(x),g(x)趋向于0
极限为e^{lim[f(x)/g(x)]}
这里
f(x)=(a^x+b^x+c^x)/3-1=(a^x-1)/3+(b^x-1)/3+(c^x-)/3
g(x)=x
f(x)/g(x)
=(a^x-1)/3x+(b^x-1)/3x+(c^x-1)/3x
lim[(a^x-1)/3x]
=lim[lga*a^x/3](罗必塔法则)
=lga/3
=lg[a^(1/3)]
那么
lim[f(x)/g(x)]
=lg[(abc)^(1/3)]
lim[(a^x+b^x+c^x)/3]^(1/x)
=e^{lg[(abc)^(1/3)]}
=(abc)^(1/3)