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Help finding an equation for the level curve

  1. Oct 3, 2005 #1
    Hey guys, I tried it out, but I just don't get it. I have to find the equation for the level curve f(x, y)=(x^2 + y^2)e^(xy); that contains the point P(1,0). By the way, e^(xy) is read e to the x times y, just in case.


    What I did, which looks wrong the whole way was:

    (x^2 + y^2)e^(xy) ---> (x^2)(e^(xy)) + (y^2)(e^(xy)) = 0

    ---> ln(x^2) + ln(e^(xy)) = (-1) ln(y^2) + ln(e^(xy))
    ---> 2ln(x) + xy = (-1) (2ln(y) + xy)
    ---> 2ln(x) = (-1)(2ln(y))


    ...and i'm stuck there. Could anyone help correct this, or if possible, help continue? Thanks a bunch.Help finding an equation for the level curve...

    --------------------------------------------------------------------------------

    Hey guys, I tried it out, but I just don't get it. I have to find the equation for the level curve f(x, y)=(x^2 + y^2)e^(xy); that contains the point P(1,0). By the way, e^(xy) is read e to the x times y, just in case.


    What I did, which looks wrong the whole way was:

    (x^2 + y^2)e^(xy) ---> (x^2)(e^(xy)) + (y^2)(e^(xy)) = 0

    ---> ln(x^2) + ln(e^(xy)) = (-1) ln(y^2) + ln(e^(xy))
    ---> 2ln(x) + xy = (-1) (2ln(y) + xy)
    ---> 2ln(x) = (-1)(2ln(y))


    ...and i'm stuck there. Could anyone help correct this, or if possible, help continue? Thanks a bunch.
     
  2. jcsd
  3. Oct 3, 2005 #2
    sorry bout the double pasting there.
     
  4. Oct 3, 2005 #3
    I believe that level curves are values of f(x,y) where f(x,y) = a constant.

    To find the level curve of f(x, y)=(x^2 + y^2)*e^(x*y) that contains the point p(1,0):

    Step 1: Evaluate f(x,y) at p(1,0) that is, f(1,0) = constant k

    Step 2: your level curve that contains the point p(1,0) is then just
    f(x,y) = k, the constant you found in step one.

    I hope this helps, if not, let me know and I'll work an example similar to the one you posted above.

    Best Regards,

    Edwin
     
  5. Oct 3, 2005 #4

    Tide

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    Science Advisor
    Homework Helper

    Why don't you use polar coordinates? Also, why are you setting the function to 0? You should be setting it to f(1, 0) -- as edwin suggested!
     
  6. Oct 4, 2005 #5
    Thanks a bunch guys...
     
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