Sep25-10, 02:56 PM
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.
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