证明lim(x,y)→(0,0),xy/根号(x²+y²)=0

题目

证明lim(x,y)→(0,0),xy/根号(x²+y²)=0

答案

因为│xy/(x^2+y^2)^(1/2)│≤0.5(x^2+y^2)^(1/2)
任给小正数ξ>0,要使│xy/(x^2+y^2)^(1/2)│＜ξ,只要(x^2+y^2)^(1/2)