lim(x趋向于0)(cosx)^[1/(xsinx)]=

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lim(x趋向于0)(cosx)^[1/(xsinx)]=
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lim(x趋向于0)(cosx)^[1/(xsinx)]=
lim(x趋向于0)(cosx)^[1/(xsinx)]=

lim(x趋向于0)(cosx)^[1/(xsinx)]=
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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