Differential Problems

Solutions

Calculate the Differential of the Following Functions:

1 Differential Exercise

2 Differential Exercise

3 Differential Exercise

4Differential Exercise

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


1

Calculate the differential:

1 Differential Exercise

Differential Operations

Differential Solution


2

Calculate the differential:

2 Differential Exercise

Differential Solution


3

Calculate the differential:

3 Differential Exercise

Differential Operations

Differential Solution


4

Calculate the differential:

4 Differential Exercise

Differential Operations

Differential Operations

Differential Operations

Differential Solution


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.

Differential Operations

Differential Operations

Differential Operations

Differential Solution


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.

Differential Operations

Differential Solution


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.

Differential Operations

Differential Operations

Differential Solution


8

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

Differential Operations

Differential Operations

Differential Solution