lim(x,y)->(0,0)xy/(根号下(x^2+y^2))

Question

lim(x,y)->(0,0) xy/(根号下(x^2+y^2))

Answer 1

利用均值不等式,0≤|xy/√(x^2+y^2)|≤1/2×√(x^2+y^2)|
1/2×√(x^2+y^2)|的极限0,由夹逼准则,原极限是0