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,](/uploads/image/z/8762935-31-5.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90%28%E5%B7%A5%E6%9C%AC%E9%AB%98%E6%95%B0%EF%BC%89lim+%5B2-%28xy%2B4%29%5E%281%2F2%29%5D%2Fxyx-%3E0y-%3E0%E8%AF%81%E6%98%8E%E5%87%BD%E6%95%B0f%28x%2Cy%29%3D%28x%2By%29%2F%28x-y%29%E5%9C%A8%E7%82%B9%280%2C0%29%E5%A4%84%E7%9A%84%E4%BA%8C%E9%87%8D%E6%9E%81%E9%99%90%E4%B8%8D%E5%AD%98%E5%9C%A8%E3%80%82%E4%B8%8A%E9%A2%98%E4%B8%8D%E7%94%A8%E7%AD%94%E4%BA%86%EF%BC%8C)
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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