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Math Help - domain of f(x,y,z)

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    domain of f(x,y,z)

    describe the domain of f(x,y,z) = sqrt(1-x^2-(y^2/9)-(z^2/4))

    i feel as if its 1>= x^2-(y^2/9)-(z^2/4) but i am not sure...can any one help???
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  2. #2
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    Quote Originally Posted by chris25 View Post
    describe the domain of f(x,y,z) = sqrt(1-x^2-(y^2/9)-(z^2/4))

    i feel as if its 1>= x^2-(y^2/9)-(z^2/4) but i am not sure...can any one help???

    Since the radicand needs to be positive we can se up the inequality

    1-x^2-\frac{y^2}{9}-\frac{z^2}{4} \ge 0 \iff x^2+\frac{y^2}{9}+\frac{z^2}{4} \le 1

    The domain is the surface and interior of an ellipseoid centered at the origin.
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