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Calc 3 homework problem need help!

  1. Oct 10, 2005 #1
    Hello guys I am not sure if I am doing this right. If you could offer any advice or point out my mistakes I would appreciate it.

    Problem: Sketch the graph of the domain of [tex]f(x,y,z) = \frac{1}{x^2+y^2-z}[/tex]

    Domain: [tex](x,y,z) \in R^3 \mid x^2+y^2 [/tex]does not equal z

    Graph: I set [tex]f(x,y,z) = 1[/tex] and solved for [tex]z[/tex]
    I got [tex]z=x^2+y^2-1[/tex] <<-- Would this be the proper graph of the domain?

    Thanks
     
    Last edited: Oct 10, 2005
  2. jcsd
  3. Oct 11, 2005 #2

    CarlB

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    No, setting [tex]f(x,y,z)=1[/tex] has nothing to do with the domain. You were right when you said that the domain is the points in R^3 where x^2+y^2 isn't equal to z. But from there you jumped in the wrong direction.

    Carl
     
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