lim(x->0) [(1+x)^(1/n)-1] / (x/n)
0/0型用洛必达法则
=lim(x->0) 1/n(1+x)^(1/n-1)/(1/n)
=lim(x->0)(1+x)^(1/n-1)
=1^(1/n-1)
=1
所以两个是等价无穷小
当x趋向于0时,证明(1+x)开根号n次方-1~n分之x
当x趋向于0时,证明(1+x)开根号n次方-1~n分之x
数学人气:396 ℃时间:2020-04-18 03:31:40
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