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

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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

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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