Module 5 : Linear and Quadratic  Approximations, Error  Estimates,  Taylor's Theorem,  Newton and Picard Methods
Lecture 14 : Quadratic approximations and error estimates [Section 14.2]
 

Let us fix a . We have to consider two cases.

Case (i):

In this case, for , we have
                      
Thus
                      
For example,
                     for all
Thus, for all
differs from at most by

Case (ii): .

In this case, for , we have
                      .
Thus,
                     
For example,
                     for

1
13