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Math Help - Differentials to estimate the maximum error

  1. #1
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    Question Differentials to estimate the maximum error

    hey guys, i really don't know where to start where to end. plz help me solve this problem

    The dimensions of a closed rectangular box are measured as 100 centimeters, 80 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.


    ___________________ square centimeters
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  2. #2
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    Quote Originally Posted by DMDil View Post
    hey guys, i really don't know where to start where to end. plz help me solve this problem

    The dimensions of a closed rectangular box are measured as 100 centimeters, 80 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.


    ___________________ square centimeters
    the surface area of the box is S=2xy + 2yz + 2zx. thus dS=2(y+z)dx + 2(x+z)dy + 2(x+y)dz. so: the maximum error in calculating S \approx 0.2 \times (360 + 400 + 360) =224 \ \text{cm}^2
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