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Homework Help: Calc III - Graphing a Function of Multiple Variables by hand

  1. Feb 18, 2012 #1
    I come across questions where I have to match the equation with its contour map and graph.


    z = sin(xy)

    z = sin(x-y)

    Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? :confused: For example, for z = sin(xy) I'm just plugging in random values for x and y... but doesn't that mean the entire xy graph should be filled then?
  2. jcsd
  3. Feb 18, 2012 #2


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    A contour of (for example) sin(xy) is a curve on the x, y plane where this function is constant. This in turn means that the product xy must be constant. So you could write

    c = xy
    y = c/x

    And for each c you get a different contour. Plotting the curves once you have them in that form is probably a little more familiar to you.
  4. Feb 18, 2012 #3


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    Set z equal to some value (-1 ≤ z ≤ 1, why?), then solve for y in terms of x.
  5. Feb 18, 2012 #4


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    If you're doing it by hand I think it's easier to do what I wrote, for a few simple c values and afterwards evaluate what z is on each curve. Of course your way works too.
  6. Feb 18, 2012 #5
    Wow, this is brilliant @_@ Thank you

    You would need a calculator for this method though, right? Inverse sin of (-1 to 1) = xy.
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