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Lim(x+y)/(x2-xy+y2)(x,y)→(∞,∞)这个怎么算Lim(x,y)→(∞,∞)(x+y)/(x2-xy+y2)
题目详情
Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算
Lim(x,y)→(∞,∞) (x+y)/(x2-xy+y2)
Lim(x,y)→(∞,∞) (x+y)/(x2-xy+y2)
▼优质解答
答案和解析
∵(x+y)/(x²-xy+y²)=(x+y)/[(x-y)²+xy]≤(x+y)/(xy)
∴0≤│(x+y)/(x²-xy+y²)│≤│(x+y)/(xy)│
≤(│x│+│y│)/│xy│
=1/│y│+1/│x│
-->0+0=0 (当(x,y)-->(0,0)时)
故原式=0
∴0≤│(x+y)/(x²-xy+y²)│≤│(x+y)/(xy)│
≤(│x│+│y│)/│xy│
=1/│y│+1/│x│
-->0+0=0 (当(x,y)-->(0,0)时)
故原式=0
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