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166E2-S09

# 166E2-S09 - MA 166 Exam 2 Spring 2009 Page 1/4 NAME Page 1...

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Unformatted text preview: MA 166 Exam 2 Spring 2009 Page 1/4 NAME Page 1 10—DIGIT PUID __ Page 2 RECITATION INSTRUCTOR —_ Page 3 Page 4 RECITATION TIME __ ’____ TOTAL _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, or any electronic devices may be used on this test. <9) 1.1/4 0 0052 :c x ‘1‘” 2' / MA 166 Exam 2 Name Spring 2009 [Hint /sec :cda: =1n|secm + tan as] + C] (10) 3' / x/tZdtﬁ (10) 4. / (xi—xwdx. Page 2/4 1 (10) 5. Find the area of the region under the curve y = 3 x + a: fromx=1t0m=2. MA 166 Exam 2 Spring 2009 Name —__ Page 3/4 a (10) 6. Find the volume of the solid of revolution obtained by rotating about the m—axis the region bounded by the curves :3 = 325, y = O and y 2: sin x, g S a: 3 11'. C: (8) 7. Determine whether the integral below is convergent or divergent, and ﬁnd its value if it is convergent. Important: You must use the deﬁnition of improper integrals. 00 2 / are—9c dm 0 (8) 8. For each of the improper integrals below, circle C if it is convergent or D if it is divergent. (You need not show work for this problem). m . (a) / sin6d6 C 27r 3 1 (b) dx C 2 3 — :17 0 dx C (c) [we 2% 2 (d) dm C MA 166 Exam 2 Spring 2009 Name —— Page 4/4 (8) 9. Find the length of the curve 3/ = g 173/2, 0 S m g 3. (9) 10. ConSider the lamina bounded by the curves y = a: and y = x2, and with density p : 1. Find the following. (a) The mass m of the lamina (b) The moment My of the lamina about the y—axis. (c) The x—coordinate Ev" of the center of mass of the lamina. (8) 11. Determine whether each sequence below converges or diverges and if it converges ﬁnd its limit. (You need not show work for this problem). (a) {(-1)”n€_"} (c) {008(mr)} (d) an 2 nsin(;1;) ...
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166E2-S09 - MA 166 Exam 2 Spring 2009 Page 1/4 NAME Page 1...

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