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Sketch level sets

  1. Sep 19, 2013 #1

    939

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    1. The problem statement, all variables and given/known data

    I am very uncomfortable with the concept of "level sets" and don't quite get what it means.

    2. Relevant equations

    y = 2(x1)^2 - (x1)(x2) + 2(x2)^2


    y = 2x1^(1/2) * x2^(1/2)

    3. The attempt at a solution

    I'm not even sure where to start... Can anyone please give me some basic knowledge of how to approach these problems?
     
  2. jcsd
  3. Sep 19, 2013 #2

    Ray Vickson

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    A level set of f(x1,x2) is the curve f(x1,x2) = constant. If z = f(x1,x2) describes a hill or mountain, a level set of f would be a path of constant elevation. That's all!
     
  4. Sep 19, 2013 #3

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    Thanks...

    So in the top example above,

    2(x1)^2 - (x1)(x2) + 2(x2)^2 = C?

    What I'm confused about also is how I would graph it...
     
  5. Sep 19, 2013 #4

    Ray Vickson

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    For a given numerical value of C, the equation describes some type of curve; you need to figure out what that curve is, and draw it. Surely you must have done problems like that in the past!
     
  6. Sep 19, 2013 #5

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    Thanks... The only thing I don't get is figuring out what the curve is when there is always two xs, i.e. y = ((x1)^(2))*((x2)^(2))... Do you use algebra to put it into a form you can understand better?

    Sorry for the newb questions...
     
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