The dimensions of a closed rectangular box are measured as 90 centimeters, 50 ce

Question

The dimensions of a closed rectangular box are measured as 90 centimeters, 50 centimeters, and 100 centimeters, respectively, with the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.

Explanation / Answer

1) ?z = ==> ?z(2, 1) = . So, the equation of the tangent plane is z - (-27) = -36(x - 2) + -18(y - 1). 2) This is done just like 1). 3) Just find the equation of the tangent plane at (x, y, z) = (-8, 4, -16) [as above] and solve for z. 4) Here, A(x,y,z) = 2xy + 2xz + 2yz. Letting x = 80, y = 50, z = 100, we see that ?x = ?y = ?z = 0.2 dA = ?A

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