Some Facts About Taylor Series....

Taylor series can be used to evaluate the value of a whole function in each point, if the functional value and its derivatives are identified at single point.  

Uses of the Taylor series for whole functions are:

        1.The sum of partial series can be used as approximations of the entire function.

        2.The representation of series reduces many mathematical proofs.

       

      In Taylor series, algebraic functions are indicated using an algebraic equation, and transcendental functions are indicated using properties which holds them, namely differential equation. Example the exponential function is equal to its own derivative and its original value is 1.

Taylor series is a  expansion of series and its function about a point.