lim(x趋向于0)(cosx)^[1/(xsinx)]=

问题描述:

lim(x趋向于0)(cosx)^[1/(xsinx)]=
1个回答 分类:数学 2014-11-16

问题解答:

我来补答
lim(x趋向于0)(cosx)^[1/(xsinx)]=lim(x趋向于0)[(1+cosx-1)^(1/(cosx-1))]^[(cosx-1)/(xsinx)]
=lim(x趋向于0)e^[(cosx-1)/(xsinx)]
=e^lim(x趋向于0)[(cosx-1)/(xsinx)]
=e^lim(x趋向于0)[-sinx/(x+xcosx)]
=e^(-0.5)
 
 
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