lim(x+y)cos(1/(x^2+y^2))且x,y趋于0

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lim(x+y)cos(1/(x^2+y^2))且x,y趋于0

lim(x+y)cos(1/(x^2+y^2))且x,y趋于0
lim(x+y)cos(1/(x^2+y^2))且x,y趋于0

lim(x+y)cos(1/(x^2+y^2))且x,y趋于0
x,y趋于0时,1/(x^2+y^2)→∞,则cos(1/(x^2+y^2))为在-1和1之间振荡的有界函数,不是无穷.
而x+y→0,

lim(x+y)cos(1/(x^2+y^2))=0