Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算

题目

Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算
Lim(x,y)→(∞,∞) (x+y)/(x2-xy+y2)

答案

∵(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...