Question

The length and width of a rectangle are measured as 58 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

Error in calculated area =
`\pm 10.3 cm^2`

Explanation:

x = 58 cm

y = 45 cm

A = x*y

delta A

= delta (x*y)

= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)

= 45(0.1) + 58(0.1)

= 103(0.1)

= 10.3 cm^2