Question

lim x趋近于无穷 y趋近于无穷 x+y / x^2-xy+y^2

Answer 1

详情如图所示

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Answer 2

因x^2+y^2≥2|xy|,所以
0≤|(x+y)/(x^2-xy+y^2)|
≤|x+y|/(x^2+y^2-|xy|
≤|x+y|/|xy|
≤1/|x|+1/|y|
且lim
(1/|x|+1/|y|)=0
故lim
[(x+y)/(x^2-xy+y^2)]=0.
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