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162E2-S2005

162E2-S2005 - MA 162 Exam 2 ’ Spring 2005 Name Student ID...

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Unformatted text preview: MA 162 Exam 2 ’ Spring 2005 Name: Student ID: Lecturer: Recitation Instructor: Recitation Time: Instructions: 1. This package contains 11 problems worth 9 points each. 2. Please supply all information requested above and on the mark—sense sheet. You get 1 point for supplying all information correctly. 3. Work only in the space provided, or on the backside of the pages. Mark your answers clearly on the scantron. Also circle your choice for each problem in this booklet. 4. No books, notes, or calculator, please. MA 162 Exam 2 Spring 2005 9 6 1. For the integral / Eda: the Midpoint Rule with n = 4 gives the approximate value 1 A. 8.5 B. 9 C. 10.5 D. 11 E. 12.5. 1 8 2. /sin_2 attcos3 :1: dz: = 0 3. Which of the following integrals are convergent? 00 1_ / sin(2t) dt. A. Nelther. 0 B. Only I. H °° sin-2t dt C. Only 11. . t3 + 1 ' D. Both are. 1 E. None of the above is correct. § x2 4. The length of the curve y = f— —3—, 1 _<. a: g 9 is 5. If masses of 3kg, 3kg, and 1kg are placed at the points (0,2), (2,0) and (~3, —3), where should a mass of 2kg be placed so that both moments ME, My of the system are 0? P V Nip—I PU ' “I NICO v F7 .0 \- NIH er—I v F3 [01" [0101 NIH MIC» MIC») NIv—I v 00 n 2 6. 23;; z n=1 A. 6 B. 2 C. 12 D. 8 E. series is divergent 7. Find the following limits. . n2 A. a = 1, b does not exist a. 11m 7 "40° 6 B. a = 0, b does not exist , V2722 + 3n , 1 b. 11m -———— C. a does not eXISt, b = —— n—wo 2n + I \/—2— D a - 0 b — 1 _ , _ ﬂ E a = O, b = 1 8. Which of the following statements are true? 00 I. If 2a,, converges, then lim an 2 0. 71—)00 Only I and II. Only I and III. Only II and III. 11:1 00 II. If lim atn = 0, then Zan converges. 11—)00 n=1 All are true. papaya? Only I is true. 71—)00 00 III. If lim an 95 0, then 2 an diverges. n=1 00 9. The series 2 n=2 00 10. The series 2 11—1 1 . n(ln n) 1 _ v2n3—n A. converges by integral test. B. converges by comparison test. 1 C. converges because lim 2 0. n—wo n(1n n) ' 1 D. diverges because lim ¢ 0 n—roo n(ln n) I E. diverges by integral test. A b l' 1 . conver es ecause 1m ———- g "#00 V2713 — n B. diverges by integral test. =0. C. diverges by comparison test. D. diverges because lim V2113 — n aé 0. fir—>00 E. converges by limit comparison test. 11. By the Alternating Series Estimation Theorem, if we approximate i (—7?” sum of the ﬁrst 4 terms, we are guaranteed an error less than or egfilal'to 1 A. 1—26 1 B. 54?)- 1 C. 2—56 1 D. '5_1§ 1 E. 56 ...
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162E2-S2005 - MA 162 Exam 2 ’ Spring 2005 Name Student ID...

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