跪求极限Y=lim (xy+1)/x^4+y^4,当(x,y)→(0,0),写下步骤,谢谢

来源:百度知道 编辑:UC知道 时间:2024/05/07 12:44:58

Y=lim (xy+1)/x^4+y^4
=lim (xy+1)/lim (x^4+y^4)
又(x,y)→(0,0),则有:
lim (xy+1)=1,(x^4+y^4)∈(0,1)
Y=lim (xy+1)/x^4+y^4
=lim (xy+1)/lim (x^4+y^4)
=∞(当(x,y)→(0,0)时)

当(x,y)→(0,0),
xy+1 -->1
x^4+y^4 -->0
Y=lim (xy+1)/x^4+y^4 =无穷大

=lim(xy+1)/x^4+y^4
<=lim(xy+1)/2(xy)^2
<=lim1/2xy+lim1/2(xy)^
趋于无穷大