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limx趋近于无穷y趋近于无穷x+y/x^2-xy+y^2
题目详情
lim x趋近于无穷 y趋近于无穷 x+y / x^2-xy+y^2
▼优质解答
答案和解析
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.
希望能帮到你, 望采纳. 祝学习进步
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.
希望能帮到你, 望采纳. 祝学习进步
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