求极限:lim xy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)$(acontent)
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求极限:limxy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)$(acontent)求极限:limxy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)$(aconten
求极限:lim xy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)$(acontent)
求极限:lim xy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)
$(acontent)
求极限:lim xy分之{[(1+xy)开3次根号]-1},(x,y)→(0,0)$(acontent)
这是一个重要极限 (1+x)开n次根号—1 趋向于x/n
所以呢
lim 分子xy/3 分母xy
结果 1/3
lim xy分之{[(1+xy)开3次根号]-1}
=limxy/[(1+xy)^(1/3)-1]
=lim t /[(1+t)^(1/3)-1]【令xy=t,t->0】
=lim t* [(1+t)^(2/3)+ (1+t)^(1/3)+1] /[(1+t)-1]
=lim [(1+t)^(2/3)+ (1+t)^(1/3)+1]
=3
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