Skip to Main Content
Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Infinite Sequences and Series 17-31
This infinite power series is called Taylor’s series.
Thus, Taylor’s series converges for all values of x for which R
n
approaches 0 as n increases without
limit.
Remark 17.2 The above infinite series represents the function for only those values of x for which R
n
approaches zero as the number of terms gets larger and larger.
17.8.1 Maclaurin’s Series
If we take a = 0 in Taylor’s series, then we obtain the Taylor’s series about 0:
f x
f
n
x f x f '
x
f ''
x
f '''
n
n
n
( )
( )
!
( ) ( )
!
( )
!
( )= =
+ + + +
=
0
0 0
2
0
3
0
0
2 3
The above series is called Maclaurin’s series.
Example 17.44 If f(x) = e
x
, then find the Taylor’s series ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Differential Equations, 3rd Edition

Differential Equations, 3rd Edition

Steven G. Krantz
Quick Calculus, 3rd Edition

Quick Calculus, 3rd Edition

Daniel Kleppner, Peter Dourmashkin, Norman Ramsey
Calculus I

Calculus I

W. Michael Kelley

Publisher Resources

ISBN: 9789353948221