The length and width of a rectangle are measured as 30cm and 24cm, respectively, with an error in measured of

at most 0.1cm in each. Use differentials to estimate the maximum error in the calculated area of rectangle.

The maximum error in the calculated area of rectangle is 5.4 cm².

Step-by-step explanation:

Given : The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in measured of  at most 0.1 cm in each.

To find : Use differentials to estimate the maximum error in the calculated area of rectangle ?

Solution :

The area of the rectangle is

The derivative of the area is equal to the partial derivative of area w.r.t. length times the change in length plus the partial derivative of area w.r.t. width times the change in width.

i.e.

Here,

Substitute the values,

Therefore, the maximum error in the calculated area of rectangle is 5.4 cm².

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