Chapters
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:
Solution of exercise 2
Calculate the differential:
Solution of exercise 3
Calculate the differential:
Solution of exercise 4
Calculate the differential:
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.
Error = 
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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