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]
2.

 Let

                    
Write down the linear and the quadratic approximations near the point . Estimate the errors.

3. 

For the following functions find the quadratic approximations near the point , and also find the error

 

bounds valid for :

1
15