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d-rock

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**Estimating Maximum Error, Odd Question? (Please Help Today!)**

## Homework Statement

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 ln(2) with maximum possible errors of |dx| = 0.1 and |dy| = 0.02. Estimate the maximum possible error in the computed value of T.

## Homework Equations

|E| <= (1/2) * M * (|x - xo| + |y - yo|) ^ 2

## The Attempt at a Solution

dT/dx = (e^y + e^-y) and dT/dy = x(e^y - e^-y)

d2T/dx2 = 0, d2T/dy2 = x(e^y + e^-y) @ (2, Ln(2)) = 2(2 + 1/2) = 5

and lastly d2T/dxy = (e^y - e^-y) @ (2, Ln(2)) = 2 - 1/2 = 1.5

So I believe the M maximum is 5, for the second derivative with respect to y.

Then, I used the equation:

|E| <= (1/2) * 5 * (|dx| + |dy|)^2 = 2.5 * (0.1 + 0.02)^2 = 0.036

So my answer was 0.036. But the book's answer is 0.31. So I am unsure what went wrong or if I overlooked something...?

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