Basic Maclaurin Series

Basic Maclaurin Series - k-1)( k-2) x 3 3! + · · ·-1...

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Basic Maclaurin Series sin x = x - x 3 3! + x 5 5! - x 7 7! + · · · = ± n =0 ( - 1) n x 2 n +1 (2 n + 1)! -∞ < x < + cos x =1 - x 2 2! + x 4 4! - x 6 6! + · · · = ± n =0 ( - 1) n x 2 n (2 n )! -∞ < x < + e x = 1 + x + x 2 2! + x 3 3! + x 4 4! + · · · = ± n =0 x n n ! -∞ < x < + sinh x = e x - e - x 2 = x + x 3 3! + x 5 5! + x 7 7! + · · · = ± n =0 x 2 n +1 (2 n + 1)! -∞ < x < + cosh x = e x + e - x 2 = 1 + x 2 2! + x 4 4! + x 6 6! + · · · = ± n =0 x 2 n (2 n )! -∞ < x < + 1 1 - x = 1 + x + x 2 + x 3 + x 4 + · · · = ± n =0 x n - 1 < x < 1 ln(1 + x )= x - x 2 2 + x 3 3 - x 4 4 + · · · = ± n =1 ( - 1) n +1 x n n - 1 <x 1 arctan x = x - x 3 3 + x 5 5 - x 7 7 + · · · = ± n =0 ( - 1) n x 2 n +1 2 n +1 - 1 x 1 (1 + x ) k = 1 + kx + k ( k - 1) x 2 2! + k (
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Unformatted text preview: k-1)( k-2) x 3 3! + · · ·-1 < x < 1 √ 1 + x = (1 + x ) 1 2 = 1 + x 2-x 2 8 + x 3 16-· · ·-1 < x < 1 arcsin x = x + x 3 2 · 3 + 1 · 3 x 5 2 · 4 · 5 + 1 · 3 · 5 x 7 2 · 4 · 6 · 7 + · · · = ∞ ± n =0 (2 n )! x 2 n +1 (2 n n !) 2 (2 n + 1)-1 < x < 1...
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This note was uploaded on 06/14/2011 for the course MATH 2415 taught by Professor Staff during the Spring '08 term at HCCS.

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