求极限lim(x~0)((e^x+e^2x+e^3x)/3)^1/xs
问题描述：
求极限lim(x~0)((e^x+e^2x+e^3x)/3)^1/x
s
答
lim(x~0)((e^x+e^2x+e^3x)/3)^1/x
=lim(x~0)e^[(ln(e^x+e^2x+e^3x)/3)/x]
=e^lim(x~0) (e^x+2e^20+3e^3x)/[(e^x+e^2x+e^3x)/3]
=e^[(1+2+3)/(1+1+1)*3]
=e^6
答
lim(x~0)((e^x+e^2x+e^3x)/3)^1/x
=lim(x~0)(e^(ln(e^x+e^2x+e^3x)/3)/x)
=e^(lim(x~0)(ln(e^x+e^2x+e^3x)/3)/x)
=e^(lim(x~0)(3(e^x+2e^2x+3e^3x)/(e^x+e^2x+e^3x))
=e^(3(1+2+3)/(1+1+1))
=e^6