Question

(e^x-1)/x极限为何为1?x趋近0

看e^x导数本身候想所能母别求导 求严谨代数证明

Answer 1

书写便我计算:lim[x→0]
x/(e^x-1)
lim[x→0]
x/(e^x-1)
令e^x-1=u则x=ln(1+u)
=lim[u→0]
ln(1+u)/u
=lim[u→0]
(1/u)ln(1+u)
=lim[u→0]
ln[(1+u)^(1/u)]
=lne
=1
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