Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(8x) Σ n = 0 Important Maclaurin series and their radii of convergence. 1 x = n=0 x" = 3 1 + x + x² + x ³ + .. ex = n=0 ∞ n! X 1 + Σ(-1)" n=0 3 + + + 1! 2! 3! 2n+1 (2n+1)! =x- 33 3! sin x = + 55 5! | R = 1 R = 8 x7 7! + R 8 = X 8 Σ(-1)". COS X = n=0 +2n (2n)! Σ(-1)" -1 tan x = n=0 = 2n+1 -1 xn In(1 + x) = Σ(−1)"−1 x n=1 ∞ k n 1 = x = x 2! - + x .4 - x 6 4! 6! + x 3 R = X 7 x + 3 + 5 7 R = 1 X 3 4 x X + 2 3 - R = 1 (1 + x)² = Σ (*) ** = n k(k − 1) 2 k(k-1)(k2) 3 = 1+kx+ x² + x + · R = 1 2! 3! n=0 n

Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(8x) Σ n = 0 Important Maclaurin series and their radii of convergence. 1 x = n=0 x" = 3 1 + x + x² + x ³ + .. ex = n=0 ∞ n! X 1 + Σ(-1)" n=0 3 + + + 1! 2! 3! 2n+1 (2n+1)! =x- 33 3! sin x = + 55 5! | R = 1 R = 8 x7 7! + R 8 = X 8 Σ(-1)". COS X = n=0 +2n (2n)! Σ(-1)" -1 tan x = n=0 = 2n+1 -1 xn In(1 + x) = Σ(−1)"−1 x n=1 ∞ k n 1 = x = x 2! - + x .4 - x 6 4! 6! + x 3 R = X 7 x + 3 + 5 7 R = 1 X 3 4 x X + 2 3 - R = 1 (1 + x)² = Σ (*) ** = n k(k − 1) 2 k(k-1)(k2) 3 = 1+kx+ x² + x + · R = 1 2! 3! n=0 n

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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