In some health centers they use the empirical formula. To calculate the surface

Question

In some health centers they use the empirical formula.

To calculate the surface area of the patient's body (in square feet), where w is the patient's weight (in pounds) and h his height (in inches).

If it is thought that measuring a patient's weight carries a percentage error of no more than 3% and the height is measured as a percentage error of no more than 2%, use differentials to estimate the largest possible percentage error that can be made when calculating with this formula , the surface area to the patient.

Explanation / Answer

given S=0.0109w0.425h0.725

dS=0.0109*0.425w0.425-1h0.725dw +0.0109*0.725w0.425h0.725-1dh

dS/S=[0.0109*0.425w0.425-1h0.725dw +0.0109*0.725w0.425h0.725-1dh]/[0.0109w0.425h0.725]

dS/S=[0.425w-1dw +0.725h-1dh]

dS/S=[0.425(dw/w) +0.725(dh/h)]

dS/S=[0.425(dw/w) +0.725(dh/h)]

patient's weight carries a percentage error of no more than 3% and the height is measured as a percentage error of no more than 2%

dS/S=[0.425(3%) +0.725(2%)]

dS/S=[1.275 +1.45] %

dS/S=2.725 %

the largest possible percentage error that can be made when calculating the surface area to the patient is 2.725%

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