Module 5 : Linear and Quadratic  Approximations, Error  Estimates,  Taylor's Theorem,  Newton and Picard Methods
Lecture 14 : Taylor's Theorem [Section 14.1]
 

is called the nth degree Taylor polynomial of around .

(ii)
 The term
 

                          

is called the -Remainder term of the Taylor 's formula for around .

 
(iii)
 In case
 

                                   ,

we say that has Taylor series around and write it as

                                    .

14.1.3

Example:

 

(i) Let

                          .

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