July 22, 2020

Chapters

- Calculate the Differential of the Following Functions:
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8

## 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?