The length and width of a rectangle are measured as 45 cm and 24 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.

dA (r) = 6.9 cm²

Step-by-step explanation:

Area of a rectangle is

A (r) = L * W (1)

Where L stands for length and W for width.

Taking differentials on both sides f equation (1)

dA (r) = W*dL + L*dW

As error in measurments are at most 0,1 cm (in each side), then the maximum error in calculating the area is

dA (r) = 24 * (0,1) (cm²) + 45 * (0,1) (cm²) ⇒ dA (r) = 2.4 + 4.5 (cm²)

dA (r) = 6.9 cm²