求函数f(x,y)=e^-xy在闭区域x^2+4y^2<=1上的最大值与最小值

求解
2025-05-10 07:47:47
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回答1:

x=sinα 2y=cosα y=cosα/2 0°<=α<=360° f(x,y)=e^-xy=e^-sinαcosα/2
f(α)=e^-sinα/4 最大值为 e^1/4 最小值为 e^-1/4