? asked in 科學數學 · 1 decade ago

微積分 多變數函數觀念題

the domain of f(x,y) = 1 / (x^2 - y^2) is {(x,y)︱y≠x}

every point on the level curve f(x,y) = c corresponds to a point on the graph of f that is c units above the xy-plane if c>0 and |c| units below the xy-plane if c<0

這些敘述對嗎?

錯的話哪裡錯?

1 Answer

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  • 1 decade ago
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    the domain of f(x,y) = 1 / (x^2 - y^2) is {(x,y)︱y≠x} 是錯的.應是

    the domain of f(x,y) = 1 / (x^2 - y^2) is {(x,y)︱y≠x, y≠-x}因為y=-x和y=x一樣會令f(x,y)的分母為零而令f(x,y)無意義。

    every point on the level curve f(x,y) = c corresponds to a point on the graph of f that is c units above the xy-plane if c>0 and |c| units below the xy-plane if c<0 是對的(檢視the level curve & the graph of f 之定義)

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