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Unformatted text preview: a 3 ( x ± a ) 2 + ²²² = 1 X n =1 na n ( x ± a ) n ± 1 2). Z f ( x ) dx = C + a ( x ± a ) + a 1 ( x ± a ) 2 2 + ²²² = C + 1 X n =0 a n ( x ± a ) n +1 n + 1 4 ex. (a). Find the power series representation of the function f ( x ) = ln(1 ± x ) : (b) Approximate ln 2 without a calculator. (excited yet?) 5 Power Series for Arctan x It can easily be shown that 1 1 + x 2 = 1 X n =0 ( ± 1) n x 2 n for ± 1 ² x ² 1 : 6 ex. (1)Find the power series representation for arctan x . (2) Evaluate arctan 1. Tonight’s homework: Write functions as power series. 7...
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 Spring '08
 Bonner
 Calculus, Power Series

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