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Unformatted text preview: 4. (6 points) Does n =1 arctan n converge or diverge? Explain. 5. (18 points) Parts a) and b) that follow refer to the power series X n =1 (-1) n (2 x + 3) n n 1 / 3 a) Find the interval of convergence for the given power series. b) For what values of x is the given series absolutely convergent? 6. (16 points) In parts a) and b) which follow, for | x | < 1 let f ( x ) = 1 1-x = n =0 x n . a) Find the power series, n =1 c n x n , equal to xf ( x ). b) Find the power series, n =0 b n x n equal to Z x 1 1 + t 4 dt. 7. (10 points) Find the Taylor series at a = 2, for f ( x ) = 1 x . 1...
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- Winter '98