Calculate the Differential of the Following Functions:

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

A square has a side of 2 m. Determine the increase in area of the square when its sides increase by 1 milimeter. Calculate the error made when using differentials rather than increases.

Exercise 6

Find the change in the volume of a cube of with edges of 20 centimeters, when each edge increases by 0.2 cm in length..

Exercise 7

Calculate the absolute and relative error made when calculating the volume of a sphere of 12.51 milimeters in diameter, measured with an instrument that shows thousandths of a centimeter.

Exercise 8

If is replaced by , what are the approximations of absolute and relative error?

Solution of exercise 1

Calculate the differential:

1

Solution of exercise 2

Calculate the differential:

2

Solution of exercise 3

Calculate the differential:

3

Solution of exercise 4

Calculate the differential:

4

Solution of exercise 5

A square has a side of 2 m. Determine the increase in area of the square when its sides increase by 1 milimeter. Calculate the error made when using differentials rather than increases.

Solution of exercise 6

Find the change in the volume of a cube of with edges of 20 centimeters, when each edge increases by 0.2 cm in length.

Solution of exercise 7

Calculate the absolute and relative error made when calculating the volume of a sphere of 12.51 milimeters in diameter, measured with an instrument that shows thousandths of centimeter.

Solution of exercise 8

If is replaced by , what are the approximations of absolute and relative error?

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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