Limln1/x(x趋近无穷大)=
(1+1/x)^x\u5f53x\u8d8b\u8fd1\u65e0\u7a77\u5927\u65f6\u7684\u6781\u9650\u662fe\uff0c\u90a3\u4e48\u5f53x\u8d8b\u8fd10\u7684\u65f6\u5019\u7684\u6781\u9650\u662f\u591a\u5c11\u5462\u8bbe y = (1+1/x)^x\uff0c\u5219 lny = x*ln(1+1/x) = ln(1+1/x)/(1/x)
lny \u662f\u4e00\u4e2a \u221e/\u221e \u7684\u6781\u9650\uff0c\u53ef\u4ee5\u4f7f\u7528\u7f57\u5fc5\u5854\u6cd5\u5219\uff1a
lim(lny)
=lim (1/x)'* 1/(1+1/x) /(1/x)'
=lim 1/(1+1/x)
=lim x/(x+1)
=lim 0/(0+1)
=0
\u7f57\u6bd5\u8fbe\u6cd5\u5219\u6c42\u5bfc
0
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