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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
题目详情
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,
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,
▼优质解答
答案和解析
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
=e^(lim(x~0)(3(e^x+2e^2x+3e^3x)/(e^x+e^2x+e^3x))
罗比达法则
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