Modul
e
5 : Linear and Quadratic Approximations, Error Estimates, Taylor's Theorem, Newton and Picard Methods
Lecture
14 : Taylor's Theorem [Section 14.1]
PRACTICE EXERCISES
1.
Find the
Taylor polynomial of
around
, that is,
when
and
is as below:
(i)
.
(ii)
.
(iii)
.
(iv)
.
(v)
.
(vi)
.
2.
Show that for all
,
(i)
.
(ii)
.
(iii)
.
3.
Let
denote the Taylor 's polynomial of order
for
at
. Prove the following:
(i)
.
(ii)
.
(iii)
.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Taylor polynomial of 
around 
, that is, 
and 
is as below: 
.
.
.
.
.
.
, 
.
.
.
denote the Taylor 's polynomial of order 
for 
at 
. Prove the following: 
.
.
.
