Module 5 : Linear and Quadratic  Approximations, Error  Estimates,  Taylor's Theorem,  Newton and Picard Methods
Lecture 14 : Taylor's Theorem [Section 14.1]
  PRACTICE EXERCISES
4.
 Let be functions having derivatives of order at such that
 

                  ,

where is a polynomial of degree If as , show that

                 .
5.
 Using exercises (3) and (4) above find for the following :
(i)
(ii)
 .
(iii)

(iv)

.
(v)
.
6.
 Using exercise (3) and 5(iv), show that for ,
 

              .

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