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

Then
                            
Thus for any ,
                            
(ii)
 Let
 

                             
Then, for ,
                           
Thus, for Taylor polynomial of around is given by

(iii)
 Let be a polynomial of degree :
 

                            .
Then

                            
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