Important Maclaurin series and their radii of convergence. 1 et 1 = = 3 x" ... x n=0 Σ x² = 1 + x + x² + x³ + •• xn n! 2 1 + + 1! + + 2! 3! R = 1 R = ∞ sinx = Σ(−1)". n=0 Σ(-1)". COS X = n=0 tan = (2n+1)! x² n (2n)! Σ(-1)"; n=0 2n+1 In(1+x) = Σ(−1)"−1x″ n=1 (1 + x)* = Σ (") x^= n n=0 n 1 = X 3! + - 2! + x 4! - 5! - x6 6! == = X - x” = 1+kx+ 7 X + R = ∞ 7! + R = ∞ 5 7 X + 3 + 5 7 R = 1 2 + ड्राल k(k − 1) - 2! X 4 4 R = 1 k(k-1)(k2) x + x + R = 1 3! Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(7x) 00 Σ Wi n = 0

Important Maclaurin series and their radii of convergence. 1 et 1 = = 3 x" ... x n=0 Σ x² = 1 + x + x² + x³ + •• xn n! 2 1 + + 1! + + 2! 3! R = 1 R = ∞ sinx = Σ(−1)". n=0 Σ(-1)". COS X = n=0 tan = (2n+1)! x² n (2n)! Σ(-1)"; n=0 2n+1 In(1+x) = Σ(−1)"−1x″ n=1 (1 + x)* = Σ (") x^= n n=0 n 1 = X 3! + - 2! + x 4! - 5! - x6 6! == = X - x” = 1+kx+ 7 X + R = ∞ 7! + R = ∞ 5 7 X + 3 + 5 7 R = 1 2 + ड्राल k(k − 1) - 2! X 4 4 R = 1 k(k-1)(k2) x + x + R = 1 3! Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(7x) 00 Σ Wi n = 0

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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