Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算
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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)
Lim(x,y)→(∞,∞) (x+y)/(x2-xy+y2)
![Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算](/uploads/image/z/19958789-29-9.jpg?t=Lim%28x%2By%29%2F%28x2-xy%2By2%29+%28x%2Cy%29%E2%86%92%28%E2%88%9E%2C%E2%88%9E%29%E8%BF%99%E4%B8%AA%E6%80%8E%E4%B9%88%E7%AE%97)
∵(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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