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Estimating maximum error

  1. Sep 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose that T is to be found from the formula T = x(e^y + e^-y), where x and y are found to be 2 and ln2 with maximum possible errors of |dx| = 0.1 and |dy| = 0.02. Estimate the maximum possible error in the computed value of T.

    2. Relevant equations
    |E| <= (0.5M)(|x-x0| + |y-y0|)^2

    3. The attempt at a solution
    I really didn't know how to approach this, because I don't understand how to find M (the upper bound). I went ahead and found the partial derivatives with respect to x and y, and the linear approximation, which were...

    T(x,y) = 5
    Tx(x,y) = 5/2
    Ty(x,y) = 3
    L(x,y) = (5/2)x + 3y - 3ln2

    I'm pretty sure the solution is something along the lines of |E| <= (0.5M)(0.1 + 0.02)^2

    My main problem is I don't understand how to find M. Any help is appreciated, thanks.
  2. jcsd
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