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Math Help - Domain and Level sets

  1. #1
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    Domain and Level sets

    Domain and Level sets-maths-2.pngLecturer decided to do an R3 domain whereas I would be used to the R2. Any suggestions?
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  2. #2
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    Re: Domain and Level sets

    I don't know what you mean by "decided to use the R2" The domain is not a "choice"! The problem says "f(x, y, z)" so f depends upon the three variables x, y, and z. The domain of the function is a subset of R^3. Of course to be able to take that square root we must have z- x^2- y^2\ge 0. What is that set?

    The "level sets" of levels 0 and 2 are the graphs of \sqrt{z- x^2- y^2}= 0 and \sqrt{z- x^2- y^2}= 2 which are equivalent to z= x^2+ y^2 and z= x^2+ y^2+ 2. What are those graphs?
    Thanks from kangaruaidhri
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  3. #3
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    Re: Domain and Level sets

    Domain is the lecturer's choice I meant!
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  4. #4
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    Re: Domain and Level sets

    Quote Originally Posted by kangaruaidhri View Post
    Domain is the lecturer's choice I meant!
    Hmm...
    Quote Originally Posted by HallsofIvy View Post
    The domain is not a "choice"!
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