limx->0(e^x+e^2+e^3)/3lim(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^6e^(lim(x~0)(3(e^x+2e^2x+3e^3x)/(e^x+e^2x+e^3x))上

Question

lim x->0 (e^x+e^2+e^3)/3
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
e^(lim(x~0)(3(e^x+2e^2x+3e^3x)/(e^x+e^2x+e^3x))上一步到这步看不懂,

Answer 1

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))
罗比达法则