Answered: POWER SERIES FOR ELEMENTARY FUNCTIONS…

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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Question

Find the first four nonzero terms of the Maclaurin series for the function by multiplying or dividing the appropriate power series. Use the table of power series for elementary functions on . Use a graphing utility to graph the function and its corresponding polynomial approximation. f(x) = e^x /(1 + x)

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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