**Approximate Value :-**

Let

**y=f(x)**Now ,

**Lt delta x--->0 (delta y)/(delta x)=dy/dx ,**therefore from the definition of the limit

as

*approaches*

**delta x**

**0 ,***approaches*

**(delta y)/(delta x)**

**dy/dx**therefore ,

**(delta y)/(delta x)=dy/dx**[approx . when

*is small]*

**delta x**or,

**(delta y)=dy/dx (delta x)**Thus ,

**(delta y)=dy/dx (delta x)**[approximately]

**Important Result Essential For Problems**:-

If

*and*

**x***are functions of time , t then*

**y**

**(dx/dt)=change of x in unit time**=rate of change of

*.*

**x**and

**(dy/dt)=change in y in unit time**=rate of change of

**y .**Also

**, (dy/dx)=(dy/dt)/(dx/dt)**