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Math Help - calculus Need urgent help

  1. #1
    dazearl
    Guest

    calculus Need urgent help

    Here's the question,
    Determine level set L(f,c) for the following
    f(x,y,z)= x2-2x+y2+z2-6y+11 ,c=5


    please help!!!!!
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  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276

    Level Set

    As we have three variables, the level set L(f,c) = {(x,y,z}|f(x,y,z)=c is a level surface. It is given by the equation x^2-2x+y^2-6y+z^2+11 = c= 5
    As this is quadratic in x, y, and z, the result is a quadric.

    We have:
    x^2-2x+y^2-6y+z^2+11 = 5
    x^2-2x+y^2-6y+z^2+6 = 0
    x^2-2x+1+y^2-6y+9+z^2+6-1-9 = 0 (completing the square for x and y)
    (x-1)^2+(y-3)^2+z^2-4 = 0
    (x-1)^2+(y-3)^2+z^2 = 2^2

    The resulting geometric surface should be easy to see (hint: remember the distance formula).

    --Kevin C.
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