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Math Help - question for func with 2 variables

  1. #1
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    question for func with 2 variables

    hi, i have a question

    consider function f(x,y) = 1 - x^2 - y^2

    sketch level curves for f(x,y) = c for c = -5,0,1

    that is what i am to do....is it possible to sketch for c = 1? because when i re-arrange to get y in terms of everything i get y = sqroot ( (1-c)/3 - (2x^2)/3 )

    which means if c = 1 we cant graph the solution, am i correct?
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  2. #2
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    Quote Originally Posted by fuzzylogic25 View Post
    hi, i have a question

    consider function f(x,y) = 1 - x^2 - y^2

    sketch level curves for f(x,y) = c for c = -5,0,1

    that is what i am to do....is it possible to sketch for c = 1? because when i re-arrange to get y in terms of everything i get y = sqroot ( (1-c)/3 - (2x^2)/3 )

    which means if c = 1 we cant graph the solution, am i correct?
    If
    f(x,y)=1~\implies~x=0~\wedge~y=0

    thus the "graph" consist of one point.

    I've attached the graph of f together with the plane z = 1.

    Perhaps it is possible to see that this plane is tangent to the paraboloid.
    Attached Thumbnails Attached Thumbnails question for func with 2 variables-par_tang.gif  
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  3. #3
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    thanks for the help! makes sense now


    also if i was to find the equation of the level curve f(x,y) = c which passes through the point (3sqrt(2),2sqrt(2)), how would i go about doing that?
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  4. #4
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    oops never mind foujnd out how to do it
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