Chapter 4: Partial Differentiation
Section 4.7: Approximations
Use differentials to estimate the maximum error in determining the area of a rectangle measured (in cm) to be 4×5, if each measurement is accurate to .1 cm.
If the length and width of the rectangle are x and y respectively, then the area of the rectangle is given by the function fx,y=x y. The error in measuring the area as 20 (i.e., 4 times 5) is approximately
Indeed, the maximum error will be either 4.1⋅5.1−20=0.91, or 3.9⋅4.9−20=0.89. Clearly, the maximum error is 0.91, exactly.
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