求极限lim「xy/(x^2+y^2)」^(x^2) (x,y)趋向于正无穷

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求极限lim「xy/(x^2+y^2)」^(x^2)(x,y)趋向于正无穷求极限lim「xy/(x^2+y^2)」^(x^2)(x,y)趋向于正无穷求极限lim「xy/(x^2+y^2)」^(x^2)

求极限lim「xy/(x^2+y^2)」^(x^2) (x,y)趋向于正无穷
求极限lim「xy/(x^2+y^2)」^(x^2) (x,y)趋向于正无穷

求极限lim「xy/(x^2+y^2)」^(x^2) (x,y)趋向于正无穷
x^2+y^2>=2xy
——》0limx,y→+∞ 0^(x^2)=0,
limx,y→+∞ (1/2)^(x^2)=0,
由夹逼定理知:
原式=0.