limx趋向0 (e^x+x)^1/x
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解决时间 2021-04-03 23:19
- 提问者网友：書生途
- 2021-04-03 19:01
limx趋向0 (e^x+x)^1/x
最佳答案
- 五星知识达人网友：白昼之月
- 2021-04-03 20:41
L=lim(x->0) (e^x+x)^(1/x)
lnL =lim(x->0) ln(e^x+x) /x (0/0)
= lim(x->0)(e^x+1)/(e^x+x)
=2
L= e^2
lnL =lim(x->0) ln(e^x+x) /x (0/0)
= lim(x->0)(e^x+1)/(e^x+x)
=2
L= e^2
全部回答
- 1楼网友：洒脱疯子
- 2021-04-03 21:31
limx趋向0 (e^x+x)^1/x
=limx趋向0 (1+e^x+x-1)^1/x
=e^lim(x->0)(e^x+x-1)/x
=e^lim(x->0)(e^x+1)/1
=e^2
=e²
=limx趋向0 (1+e^x+x-1)^1/x
=e^lim(x->0)(e^x+x-1)/x
=e^lim(x->0)(e^x+1)/1
=e^2
=e²
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