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