求极限(工本高数)lim [2-(xy+4)^(1/2)]/xyx->0y->0证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。上题不用答了,

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求极限(工本高数)lim [2-(xy+4)^(1/2)]/xyx->0y->0证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。上题不用答了,

求极限(工本高数)lim [2-(xy+4)^(1/2)]/xyx->0y->0证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。上题不用答了,
求极限(工本高数)
lim [2-(xy+4)^(1/2)]/xy
x->0
y->0
证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。上题不用答了,

求极限(工本高数)lim [2-(xy+4)^(1/2)]/xyx->0y->0证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。上题不用答了,
证明函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在.
当 点(x,y)沿着 直线 y = kx (k 为不等于 1的任意实数)趋于(0,0)时,
lim f(x,y)=lim (x+ kx)/(x- kx)
x->0
y->0
= (1+k)/(1-k)
当k取不同值时,上述极限的值不唯一,所以极限不存在.

∵lim(x->0){lim(y->0)f(x,y)}=lim(x->0){lim(y->0)[(x+y)/(x-y)]}
=lim(x->0)(x/x)
=1
lim(y->0){lim(x->0)f(x,y)}=lim(y->0){...

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∵lim(x->0){lim(y->0)f(x,y)}=lim(x->0){lim(y->0)[(x+y)/(x-y)]}
=lim(x->0)(x/x)
=1
lim(y->0){lim(x->0)f(x,y)}=lim(y->0){lim(x->0)[(x+y)/(x-y)]}
=lim(y->0)[y/(-y)]
=-1
∴两个单极限都存在,而累次极限不相等
故函数f(x,y)=(x+y)/(x-y)在点(0,0)处的二重极限不存在。

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