ma241exam4-c

ma241exam4-c - X n =1 ( 1 5 ) n n ( x 3) n 1 4. Determine...

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Spring 2007 Therkelsen MA 241 - Exam 4 (C) Instructions Use a blue examination book to answer all parts for each problem below. Be sure to write your name and test form (C) on the front cover of the blue book. Please do not answer more than one problem per page. Circle or box all Fnal answers (partial credit may be given, but only for work shown). No graphing calculators, cell phones, PDAs, etc. For problems 1, 2, and 4, you must justify your answer — correct answers without justi±cation will not receive full credit. For problems 5-7, your answer must either be in notation or must include at least the ±rst four non-zero terms. Include this sheet when submitting your exam book. Problems 1. Determine whether each series is convergent or divergent. (a) n =1 3+( 1) n n n (b) n =1 n 1 n 5 n 2. Determine whether each series is convergent or divergent. (a) n =1 ( 1) n cos ( 1 n ) n (b) n =0 ( 1) n n 2 8+6 n 2 3. ±ind the radius of convergence and interval of convergence for the given power series.
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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.

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ma241exam4-c - X n =1 ( 1 5 ) n n ( x 3) n 1 4. Determine...

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