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Trouble Graphing Multivariable Functions!

  1. Sep 20, 2011 #1
    So the function I'm working with is:

    f(x,y) = 1/sqrt(1-x^2-4y^2)

    First, they want me to find the Domain and Range, which I found to be:
    D: x^2 + 4y^2 < 1
    R: (0,1]
    Then they want me to sketch level curves and cross sections, then sketch f(x,y)
    I'm having trouble with the sketching, I understand the concept of level curves, but when I make f(x,y) = k I'm not quite sure where to go from here... Does anyone have any graphing tips that I could use? Thanks!
  2. jcsd
  3. Oct 10, 2011 #2
    i wouldn't mind some insight on this as well.
  4. Oct 10, 2011 #3


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    You know that 0 ≤ x2 + 4y2 because x2 & y2 are each non-negative.

    ∴ 0 ≤ x2 + 4y2 > 1

    So to find level curves, you must choose k so that 0 ≤ 1/k ≤ 1 .
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