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Unformatted text preview: Samadhi Gunasekera Senarath Dias Widhanaral Assignment 3 MATH262, Fall 2009 due 10/18/2009 at 11:59pm EDT. You may attempt each problem a maximum of 7 times. 1. (1 pt) The function f ( x ) = 3 ( 1 9 x ) 2 is represented as a power series f ( x ) = ∞ ∑ n = c n x n . Find the first few coefficients in the power series. c = c 1 = c 2 = c 3 = c 4 = Find the radius of convergence R of the series. R = . Correct Answers: • 3 • 54 • 729 • 8748 • 98415 • 0.111111111111111 2. (1 pt) The function f ( x ) = 9 x arctan ( 7 x ) is represented as a power series f ( x ) = ∞ ∑ n = c n x n . Find the first few coefficients in the power series. c = c 1 = c 2 = c 3 = c 4 = Find the radius of convergence R of the series. R = . Correct Answers: • • • 63 • •1029 • 0.142857142857143 3. (1 pt) Compute the 9th derivative of f ( x ) = cos ( 4 x 2 ) 1 x 3 at x = 0. f ( 9 ) ( ) = Hint: Use the MacLaurin series for f ( x ) ....
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 Spring '08
 FABER
 Power Series, Taylor Series, Gunasekera Senarath Dias Widhanaral

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