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Unformatted text preview: Math 1B, Final Examination N.Reshetikhin, May 13, 2005 P roblem 1 2 3 4 5 6 7 8 9 10 11 12 T otal P oints 10 15 15 15 15 15 15 15 15 10 15 20 175 Grade Students Name: GSIs name: Students i.d. number: 1.( 10 pnts ) Evaluate the integral Z e x dx 1 2.( 15 pnts ) Evaluate the integral Z 1 ( t 2 1)( t 1) dt 2 3.( 15 pnts ) Indicate which of the following statements are true and which are false. Do not show your work. 1. Z 1 sin 2 x x 3 dx converges by comparison test with Z 1 1 x 3 dx . 2. Z 1 sin( x 2 ) x dx diverges by comparison test with Z 1 1 x dx . 3. Z 2 1 dx ( x 1) 2 dx is a convergent improper integral. 4. Z  1 x 2 dx is a divergent improper integral. 5. Z ln( x ) ( x + 1) 3 / 2 dx is a convergent improper integral. 3 4.( 15 pnts ) Find the radius and the interval of convergence of the power series X n =1 n 1 ( n + 2)(2 n + 5) x 2 n 4 5.( 15 pnts ) State whether the following series is absolutely convergent, con ditionally convergent, or divergent. Do not show your work.ditionally convergent, or divergent....
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This note was uploaded on 06/26/2010 for the course MATH 58455 taught by Professor Daniel during the Fall '09 term at University of California, Berkeley.
 Fall '09
 DANIEL

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