# 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?

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To estimate the maximum error in calculating the surface area of the box using differentials, you can use the formula for the differential of a function. For a rectangular box, the surface area formula is ( S = 2lw + 2lh + 2wh ), where ( l ), ( w ), and ( h ) represent the length, width, and height of the box, respectively.

First, find the partial derivatives of the surface area formula with respect to each dimension (( l ), ( w ), and ( h )).

Then, calculate the differential of the surface area using the partial derivatives and the given errors in the measurements (( \Delta l ), ( \Delta w ), and ( \Delta h )).

Finally, substitute the given measurements and errors into the differential formula to find the estimated maximum error in the surface area calculation.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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