POWER SERIES FOR ELEMENTARY FUNCTIONS Interval of Function Convergence =1- (x - 1) + (x – 1) – (x – 1} + (x – 1)* – -..+ 0

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.2: Real Numbers
Problem 90E
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Find the Maclaurin series for the functiong(x) = 2 sin x3.

Use the table of power series for elementary functions

POWER SERIES FOR ELEMENTARY FUNCTIONS
Interval of
Function
Convergence
=1- (x - 1) + (x – 1) – (x – 1} + (x – 1)* – -..+
0 <x < 2
1
= 1-x+x - x
1+x
x* - x* + -.- + (-1)x* + .--·
-1 <x < 1
In x = (x – 1) – - 1F , k - 1) _ (x – 1)*
(-1)--"(x – 1)*
+
+
+
+ ..
0 <xs 2
2
3
* = 1+x +
- 00 <x< o
+
(-1)"x**
sin x = x-
- 00 <x< o
+
(2n + 1)!
(-1)* x
(2n)!
COs x = 1 -
- 00 <x < o
+
6!
(-1)* x'**1
arctan x = x-
-1 sxs1
+
+
2n + 1
1-3- 5x
2 -4 - 6- 7
(2n)lx*+
(2"n!)(2n + 1)
(* - 1)- -- (* - n+ 1)x*
1. 3x
+
arcsin x =x +
-1 sxs1
+
+
+
2-3
2 -4 - 5
* – 1)x, k(k –- 1)(- 2)r
(1 + x)* = 1+ kx +
-1 <x < 1*
+
2!
3!
n!
* The convergence at X= 1 depends on the vale of R.
Transcribed Image Text:POWER SERIES FOR ELEMENTARY FUNCTIONS Interval of Function Convergence =1- (x - 1) + (x – 1) – (x – 1} + (x – 1)* – -..+ 0 <x < 2 1 = 1-x+x - x 1+x x* - x* + -.- + (-1)x* + .--· -1 <x < 1 In x = (x – 1) – - 1F , k - 1) _ (x – 1)* (-1)--"(x – 1)* + + + + .. 0 <xs 2 2 3 * = 1+x + - 00 <x< o + (-1)"x** sin x = x- - 00 <x< o + (2n + 1)! (-1)* x (2n)! COs x = 1 - - 00 <x < o + 6! (-1)* x'**1 arctan x = x- -1 sxs1 + + 2n + 1 1-3- 5x 2 -4 - 6- 7 (2n)lx*+ (2"n!)(2n + 1) (* - 1)- -- (* - n+ 1)x* 1. 3x + arcsin x =x + -1 sxs1 + + + 2-3 2 -4 - 5 * – 1)x, k(k –- 1)(- 2)r (1 + x)* = 1+ kx + -1 <x < 1* + 2! 3! n! * The convergence at X= 1 depends on the vale of R.
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