In this tutorial we shall be concerned with the application of differentials to approximate any real problem. Now we consider an example
The diameter of a tree was 8 inches. After one year the circumference of the tree increased by 2 inches. How much did
(i) the diameter of the tree increases?
(ii) the cross-section area of the tree change?
Let be the radius of the tree, then its circumference is
Taking the differential of the above equation (i), we have
Since the change in the circumference is , so equation (ii) gives
This shows that the diameter of the tree is increased by inches.
If the cross-section area of the tree is , then
This shows that the change in the cross-section area of the tree is .