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二重极限lim_{x→+∞y→+∞}[xy/(x²+y²)]
^x2y2=_____.

0. 解析: 当x﹥0,y﹥0时，0﹤xy/(x²+y²)≤1/2，从而0﹤ [xy/(x²+y²)]x²y²≤(1/2)x ²y²由于lim_{x→+∞y→+∞}0=lim_{x→+∞y→+∞}(1/2)x²y²=0,所以lim_{x→+∞y→+∞2+y²)]x²y²=0 由于limx→+∞y→+∞0=limx→+∞y→+∞(1/2)x²y²=0,所以limx→+∞y→+∞2+y²)]x²y²=0}