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Unformatted text preview: X n =1 ( 1 5 ) n n ( x 3) n 1 4. Determine whether each series is absolutely convergent, convergent (but not absolutely convergent), or neither. (a) n =1 ( 11) n n ! (b) n =1 a n , where a 1 = 1 and a n +1 = n 2 ln( n +1) a n 5. Find a power series representation for the given function. f ( x ) = x 2 3 x + 1 6. Find the Maclaurin series for the function. (Do not show that R n ( x ) 0.) f ( x ) = x 3 cos(4 x ) 7. Evaluate the indenite integral as an innite series. (Dont forget to include the constant of integration!) Z 2 x 1 x 5 dx 100 points total: 20 points for 1,2,4; 10 points for 3,5,6,7 Extra Credit: Show that the function f ( x ) = X n =0 ( 1) n (2 n )! x 2 n is a solution of the dierential equation f 00 ( x ) + f ( x ) = 0. (5 pts) (Note: The interval of convergence is ( , ) you do not need to show this.) 2...
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This note was uploaded on 01/25/2011 for the course MA 241 taught by Professor Mccollum during the Spring '08 term at N.C. State.
- Spring '08