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

来源:学生作业帮助网 编辑:作业帮 时间:2024/06/17 01:22:19
Lim(x+y)/(x2-xy+y2) (x,y)→(∞,∞)这个怎么算Lim(x,y)→(∞,∞) (x+y)/(x2-xy+y2)
x)ըЮר0ҭԮ4TШЩ|6IQ< |5=|t4% $e:B#A+ lhG[ajťF`IS"Q[ Ӯ}Թf)M J* A +X+XS$P Sak*`v ON(acl6Mm}7~[<;hڀ9(l

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

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