(lim) x/(x-y)
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(lim) x/(x-y)
(lim) x/(x-y)
(lim) x/(x-y)
令y=kx,
则x/(x-y)=x/[(1-k)x] = 1/(1-k).
lim_{x->0}{x/[(1-k)x]} = 1/(1-k).
随着k的不同取值,lim_{x->0}{x/[(1-k)x]}的取值也不同.
因此,lim_{x->0,y->0}[x/(x-y)]不存在.
【若存在,则应满足唯一性,应该在y=kx时,极限唯一.】
原题极限不存在.
1
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