Power Series

Power Series - Power Series for Elementary Functions...

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AUSTIN COMMUNITY COLLEGE RIVERSIDE LEARNING LAB Last revised 21-Aug-06 Power Series for Elementary Functions I n t e r v a l o f C o n v e r g e n c e () ( ) = + −− −+ + 234 1 1 1 1 1 1 ... 1 1 ... nn xx x x x x < < 02 x =− + − + − + +− + + 2345 1 1 ... 1 ... 1 n n xx x x x x x << 11 x () ( ) −−− =− + + + + 1 111 1 1 ln 1 ... ... xxx x n < x = + +++++ ++ 1 ... ... 2! 3! 4! 5! ! n x xxxx x ex n −∞< <∞ x + =− + − + −+ + + 21 3579 1 sin ... ... 7! 9! 2 1 ! n n x n x =− + − + − + + 2 2468 1 cos 1 ... ... 6! 8! 2 ! n n x x n x + + + 1 arctan ... ... n n x n ≤≤ x + ⋅⋅ =+ + + + + 35 7 2 13 135 arcsin ... ... 23 235 2467 2!2 1 n n nx x x ( ) += + + + + + 23 4 2 3 1 1
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