求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.

求极限lim(x,y)→(+∞,+∞) [(xy)/(x²+y²)]^(xy)
解：[(xy)/(x+y)²]^(xy)?[(xy)/(x²+y²)]^(xy)?(xy/2xy)^(xy)
左边=(x,y)→(+∞,+∞) lim[(xy)/(x+y)²]^(xy)=(x,y)→(+∞,+∞) lim[(xy)/(x²+2xy+y²)]^(xy)