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]
14.2
 Quadratic approximations
14.2.1
 Definitions:
 

For , the Taylor 's polynomial

                      

is called the quadratic approximation of for near , and is also denoted by .

14.2.2
 Examples:
(i)
 Consider the function
 

                     .

Then,      
                    

Thus, for near ,

                  .

For example for ,

                .
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