# Estimating maximum error

by alsvt
Tags: error, estimating, maximum
 P: 4 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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