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How to calculate level curves

  1. Oct 31, 2011 #1
    I am being asked to calculate level curves for the following equation:
    f(x,y)=e^-(2x^2+2y^2) but I do not know where to start. Any advice on first steps would be greatly appreciated.
  2. jcsd
  3. Oct 31, 2011 #2


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    Set e^-(2x^2+2y^2) = c, where c is a constant. Solve for x or y.

    Once you do that, see if you can come up with a more general solution.
  4. Nov 1, 2011 #3


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    One obvious point: if [itex]e^{-(2x^2+ 2y^2)}= c[/itex] then [itex]-(2x^2+ 2y^2)= ln(c)[/itex] so that [itex]x^2+ y^2= -ln(c)/2[/itex] which is only possible if -ln(c)< 0 which means 0< c< 1. What figures will level curves be?
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