x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ]

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x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ]
x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ]

x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ]
x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ]
=lim(x趋向0)(-x)/x
=-1

x趋向0 lim [ ln (1-x) / (e ^ x-1 ) ] 看一下，明显的0/0开型，分子分母分别求导：
lim(x->0) [ ln (1-x) / (e ^ x-1 ) ]
=lim(x->0)(1/(1-x)*(-1))/e^x
=-lim(x->0)1/e^x(1-x)
=-1/e^0(1-0)
= -1

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