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Unformatted text preview: Math 1B, Final Examination N.Reshetikhin, May 18, 2004 Student’s Name: TA’s name: Student’s i.d. number: 1. 10 pnts Evaluate the integral x 3 e x 2 dx 1 2. 15 pnts Evaluate the integral 1 ( t 2 1)( t 1) dx 2 3. 15 pnts Indicate which of the following statements are true and which are false. Do not show your work. 1. ∞ 1 sin 2 x x 3 dx converges by comparison test with ∞ 1 1 x 3 dx . 2. ∞ 1 sin( 1 x ) x dx diverges by comparison test with ∞ 1 1 x dx . 3. 2 1 dx ( x 1) 2 dx is a convergent improper integral. 4. ∞∞ 1 x 2 dx is a divergent improper integral. 5. ∞ 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 ∞ n =1 n 1 ( n + 2)( n + 3) ( x 1 2 ) n 4 5. 15 pnts State whether the following series is absolutely convergent, condi tionally convergent, or divergent. Do not show your work....
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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 Berkeley.
 Fall '09
 DANIEL

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