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Find the maximum value of a rectangular box that can be inscribed in an ellipsoid

  1. Mar 26, 2012 #1

    s3a

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    "Find the maximum value of a rectangular box that can be inscribed in an ellipsoid.."

    1. The problem statement, all variables and given/known data
    Find the maximum value of a rectangular box that can be inscribed in an ellipsoid
    x^2 /4 + y^2 /64 + z^2 /81 = 1
    with sides parallel to the coordinate to the coordinate axes.


    2. Relevant equations
    Lagrange Multiplier method and partial differentiation.


    3. The attempt at a solution
    My attempt is attached as MyWork.jpg. I feel like I should have the correct answer but I did something wrong and I would appreciate it if someone could point out my mistake as well as tell me why it's wrong.
     

    Attached Files:

  2. jcsd
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