Question

The length and width of a rectangle are measured as 50 cm and 45 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.

Answer 1

4.5 cm ^ 2

Explanation:

We have the following partial derivative, knowing that the area is A = x * y:

dA = (dpA / dpx) * dx + (dpA / dpy) * dy = y * dx + x * dy

and that | delta x | <= 0.1, | delta and | <= 0.1. We then use dx = 0.1 and dy = 0.1, with x = 50, y = 45;

So the maximum error in the area would be:

dA = y * dx + x * dy = 50 * 0.1 + 45 * 0.1 = 5 + 4.5 = 9.5

In other words, the maximum error is 4.5 cm ^ 2