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Math Help - Finding Domain of a function

  1. #1
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    Finding Domain of a function

    Find the domain of the function f(x,y) = square root(y) + square root(25-x^2 - y^2)

    square root(y) is defined only when y equal or > then 0.
    square root(25-x^2 - y^2) is defined only when 25> or equal to x^2+y^2

    so the domain of f is {(x,y) | y>,eqaul to 0, x^2+y^2<,equal to 25}

    Did I make a mistake here?
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  2. #2
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    To simplify the description of the domain, we may note that

    x^2+y^2=5^2

    is the equation of a circle of radius 5 in the xy-plane centered at the origin.
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  3. #3
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    so how does that change my domain i had written? I dont understand
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  4. #4
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    Quote Originally Posted by andreaspohle View Post
    so how does that change my domain i had written? I dont understand
    It doesn't change it; it simply makes it easier to "see", that the domain of the function is the "top half" (in the first and second quadrants) of the circle of radius 5 centered at (0,0).
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