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]
(ii)
 Consider the function
 

                    .

Then

                    .
Thus, near , has quadratic approximation
                    .

(iii)
 Let   
                       
Then,
                    
Thus, near , has quadratic approximation:
                    
For example, this given
                    
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