166E2-S07 - MA 166 EXAM 2 Spring 2007 Page 1/4 NAME 18...

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Unformatted text preview: MA 166 EXAM 2 Spring 2007 Page 1/4 NAME / 18 10—DIGIT PUID / 32 /28 RECITATION INSTRUCTOR _ / 22 RECITATION TIME /100 DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4 . 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. _ 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators nor any electronic devices may be used on this test. Find the integrals in problems 1—5. (8) 1. (10) 2. / tan3 ac sec ac d1: 2 x / (a2 _$2)3/2 dx MA 166 Exam 2 Spring 2007 Name t d (10) 3. C_OS dtm<Hintzd — In | seczz: + tanx| : sec :10) V1 +sin2t 2 (I: ‘ 4. Page 2/4 MA 166 Exam 2 Spring 2007 Name ______—_ Page 3/4 (9) 6. Determine the constants in the partial fraction decomposition: 3x2+2x—1 _ A +B:1:+C' (x—2)(m2+2)_x—2 $2+2 (19) 7. Determine Whether each integral is convergent or divergent. Find its value if it is convergent. Important: You must use the definition of improper intergrals. a.) [jgfidm 0° 1 1 1+932 (12) (10) MA 166 Exam 2 Spring 2007 Name ——— Page 4/4 8. Consider the lamina bounded by the lines :13 + y = 1, a: = 0, and y = 0 and with density p = 1. Find the following. (a) The mass m of the lamina. m : (b) The moment My of the lamina about the y—axis. My 2 (c) The moment Mm of the lamina about the x—axis. M3; = (d) The center of mass (35, y) of the lamina. 9. Determine whether the sequence converges or diverges. If it converges, find the limit. (You need not show work for this problem.) :1 (c) an 2 In (2714: > I l we} i 3n (8) a” : 2n(100) L ...
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