作业帮求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy,
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![求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy,](/uploads/image/z/1560753-9-3.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90lim%28x%2Cy%29%E2%86%92%28%2B%E2%88%9E%2C%2B%E2%88%9E%29+%5B%28xy%29%2F%28x%5E2%2By%5E2%29%5D%5Exy.%E6%B1%82%E6%9E%81%E9%99%90lim%28x%2Cy%29%E2%86%92%28%2B%E2%88%9E%2C%2B%E2%88%9E%29+%5B%28xy%29%2F%28x%5E2%2By%5E2%29%5D%5Exy%2C)
求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy,
求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.
求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy,
求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy.求极限lim(x,y)→(+∞,+∞) [(xy)/(x^2+y^2)]^xy,
求极限lim(x,y)→(+∞,+∞) [(xy)/(x²+y²)]^(xy)
[(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)
=(x,y)→(+∞,+∞) lim[1/(x/y+2+y/x)]^(xy)≦(x,y)→(+∞,+∞) lim(1/4)^(xy)=0
右边=(xy/2xy)^(xy)=(1/2)^(xy)=0
∴lim(x,y)→(+∞,+∞) [(xy)/(x²+y²)]^(xy)=0
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