2.Geometric meaning of the differential

1. 2.4 The differential 1.Concept of the differential 2.Geometric meaning of the differential 3.Rules of operations on differentials 4.Appliction of the differential in approximate computation

2. 1.Concept of the differential

3. and is called Definition 2.4.1 ( A is a constant independent of △x) then is said to be differentiable at Denoted by namely

5. Th2.4.1 The relation of derivable and differentiable: is derivable at and i.e.

6. when is very small, 2.Geometric meaning of the differential the increment of the ordinate of the tangent then the quotient of the differentials so

7. 3.Rules of operations on differentials since So it is easy to know:

8. 1. if u(x) , v(x) are both diffierential,then (Cis a constant) 2.The differential of a composite function are derivable respectively, is differentiable and then The invariance of the differential form

9. Example 2. Suppose find Example 3. Fill the blanks:

10. Application of the differential in approximate computation when is very small, we get the approximate equality: linear approximate request:

11. is small, In particular Useful formula:

12. ExampleFind the approximate value for Sou: let taking then 机动 目录 上页 下页 返回 结束

13. Example find an approximate value for Sou: 机动 目录 上页 下页 返回 结束

14. find 3. If