The length and width of a rectangle are measured as 42 cm and 38 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

d(A) = 8 cm²

Step-by-step explanation:

Area of a rectangle is:

A(r) = L * w

L is the length, and w is the width, then

d(A) = L* dw + w*dl    

From problem statement we know:

L = 42 cm         w = 38 cm

With an error in measurement of 0,1 cm in each case, then

dw = dl = 0,1 cm

And

d(A) = 42*0,1 + 38*0,1    ⇒  d(A) =  4.2 + 3.8    ⇒    d(A) = 8 cm²

(-5,-28)

i graphed to on desmos.