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sinx = Σ(-1)" #=0 Cos X= tan Σ(1)", #=0 In(1+x) = (2n + 1)! 8 외 n = 0 2 (2n)! =X + =X • Σ(-1)" 2n +1 -Σ(-1²-¹=x-²+²- n=1 (1 + x)² = Σ (₁) x² = 1+ kx + ! #=0 15 1 6! X k(k-1) 2! + 2 x² + k(k-1)(K-2) 3! x² +.... R = ∞ R = ∞ R=1 R=1 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(9x) R=1

sinx = Σ(-1)" #=0 Cos X= tan Σ(1)", #=0 In(1+x) = (2n + 1)! 8 외 n = 0 2 (2n)! =X + =X • Σ(-1)" 2n +1 -Σ(-1²-¹=x-²+²- n=1 (1 + x)² = Σ (₁) x² = 1+ kx + ! #=0 15 1 6! X k(k-1) 2! + 2 x² + k(k-1)(K-2) 3! x² +.... R = ∞ R = ∞ R=1 R=1 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(9x) R=1

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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Important Maclaurin series and their radii of convergence. Σx"=1+x+x² + x³ +... 1-x #=0 - COS X = n=0 sin.x = (-1)"7 =0 = 1+ #=0 Σ(-1)", ²0+1 (2n + 1)! X 1! 2! Σ( n = 0 (2n)! x² x³ 3! tan ¹x=(-1)"; (² + x)² = Σ (^) x² m=0 + =x- = 1. +... x³ 3! 5! x² 14 + 2! 4! 6! ---+ 5 - $ + $ - - 1+2 In(1+x) = [(-1)^-¹¹ = x + #=1 x² 2 3 4 x"=1+kr+ 7! k(k-1) 2! + X +... x² + k(k-1) (k-2)x³+.. 3! R = 1 R = ∞ R=00 R = ∞ R=1 R=1 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(9x) R = 1
Transcribed Image Text:Important Maclaurin series and their radii of convergence. Σx"=1+x+x² + x³ +... 1-x #=0 - COS X = n=0 sin.x = (-1)"7 =0 = 1+ #=0 Σ(-1)", ²0+1 (2n + 1)! X 1! 2! Σ( n = 0 (2n)! x² x³ 3! tan ¹x=(-1)"; (² + x)² = Σ (^) x² m=0 + =x- = 1. +... x³ 3! 5! x² 14 + 2! 4! 6! ---+ 5 - $ + $ - - 1+2 In(1+x) = [(-1)^-¹¹ = x + #=1 x² 2 3 4 x"=1+kr+ 7! k(k-1) 2! + X +... x² + k(k-1) (k-2)x³+.. 3! R = 1 R = ∞ R=00 R = ∞ R=1 R=1 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(9x) R = 1
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