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The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box. (Round your answer to one decimal place.)

The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box. (Round your answer to one decimal place.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box. (Round your answer to one decimal place.)

Expert Solution
Step 1

For a function y=fx, ∂y,∂x,dy and dx represents partial derivative of y and x and then differential of y and x. 

lim∂x→0∂y∂x=dydx

when change in x is very small partial derivative of y with respect to x is same as differentiation of y with respect to x.

∂y=dydx∂x

∂x is known as error in x.

 

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