Question

Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算

Answer 1

∵(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