How do you use differentials to estimate the maximum error in calculating the surface area of the box if the dimensions of a closed rectangular box are measured as 60 centimeters, 100 centimeters, and 90 centimeters, respectively, with the error in each measurement at most .2 centimeters?
1 Answer
Let's call the measurements
Then the total surface area will be
If we include the differences and set these to
Subtract the original surface area
Since
For maximum error
Answer : the maximum error in surface area is
(On a calulated area of
Remark : if we had taken the
This is way below the significance range.