# Differential Problems

### Solutions

#### Calculate the Differential of the Following Functions:

1

2

3

4

5A 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.

6Find the change in the volume of a cube of with edges of 20 centimeters, when each edge increases by 0.2 cm in length..

7Calculate 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.

8If is replaced by , what are the approximations of absolute and relative error?

## 1

Calculate the differential:

1

## 2

Calculate the differential:

2

## 3

Calculate the differential:

3

## 4

Calculate the differential:

4

## 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.

## 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.

## 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.

## 8

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