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Solutions-166E3-S02

Solutions-166E3-S02 - (15 MA 166 EXAM 3 Spring 2002 Page...

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Unformatted text preview: (15) MA 166 EXAM 3 Spring 2002 Page 1/4 NAME QEADlIflBJEL STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, 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. . Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers. 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 or calculators may be used on this test. V DO 1. Circle the letter of the correct response. (You need not show work for this problem). 00 (a) Which of the following statements are always true for any series 21 an with 7),: positive terms? 00 00 (I) If lim an 2 0, then 2 an converges. Nat Lf‘U~£., Z J; Aiuzv es n—)oo n=1 ht, 00 (II) If lim {Van = %, then Elan converges. True . Rodi: Zele 17,—)00 n: n 5 0° . °° (III) If lim “T = —, then 2 a... dlverges. 12...... com)...” Wu, .L n—-)oo — 6 n=1 1,:1 "(71 fl wlm'dn oiz‘vnges m3. um. limit mmFar-x‘liggn test - an+1 _ 0° . (IV) If 11m — 1, then “21 an diverges. Not” tm 18‘ ' Rana tea}: {hwmmsgvt n—mo an J— EN; anex»%€a A. (II) and (IV) only B. (I), (II) and (III) only C. (I) and (III) only E23 ® (II) and (111) only E. all (b) Which of the following series converge? (I) wnvevcécs. Co mParigoaum test) n ampules with 2’1 (I) Z W (H) 22 W n1! n'i/z CflHV£\"2-e%, Ln'vm't Carrlloqn55o*rr Test M ) (I) " with J5“ (111)1—3,1 +3i—31—+3i—... Wm m > \/§ x/g x/ZI \/5 convex—ram. Altccvies Test A. (I) and (II) only B. (I) and (III) only C. (II) and (III) only D. (III) only [:7] ® all MA 166 Exam 3 Name Spring 2002 Page 2 /4 (20) 2. Determine whether each series is convergent or divergent. You must show all necessary work and write your conclusion in the small box. For Problems W0») amt} 2(5) QM“ WYSI it" I} Wrowfi‘ "-9 O P?) [AV Frckl‘am 1 " check work We ‘CN'Z‘ mCD .L YI to" V. 0“ div. ()i__—1__ a “:1 e/n(n-+1)oz+-2) Show all necessary work here: {D diverges (P-58ri:C)s/ ’32)) VIII W hm, lln (n+4) (\M 2) h—pm ' 1 3“] n Z 1 TrO By the Rim i 1 co mpoufi son test, the series is (LL Day. 00.: n1; By the \(‘qx‘m‘r’ test MA 166 Exam 3 Spring 2002 Name _________._______ Page 3/4 00 _1 n——1 (10) 3. Consider the convergent alternating series n. n=1 (a) Write out the first six terms of the series. 1 ’ 23+":1i 4% ‘5! 63 Row L a, ,L l. . / 1 - i. + «a m ~—-« Jr“ —’-' -' ——-‘ 2 G 2.4“ 120 7‘20 (b) Find the smallest number of terms that we need to add in order to estimate the sum of the series with error < 0.01. (3) _L *< 0. or @ 12° 4 m A, > o, o I “’ 24- oo “1 71—1 (10) 4. Determine whether the series 2 -(——2— is absolutely convergent, conditionally n=1 nfi convergent, or divergent. You must justify your answer. . v «mloiem . (9) 5. Find the sum of each series if it is convergent, or write divergent in the box. No partial credit. on <> i 1 h i “L‘”:‘L” ———’“* O a e :— ’_ 2’3— (in 71" 3 ":1 34:1 9’1) e '92 e 1 <b>§2:<-%>" : Ba— <33 MA 166 Exam 3 Spring 2002 Name Page 4/4 69 Jud) c' (LVN. Von s" n (A Pnigsinék \qere (xx-«A QP’a-QAYS lei-6" 0‘“ 00 (16) 6. Find the interval of convergence of the power series Zn3(x -— 5)". Don’t forget to 71:1 test for convergence at the end points of the interval. You must show all work. Palm Jich 'x«5 Ham “‘5‘” fi' two la. mi —: W (MTV-Bl : \x—sl @ warms? wow-m n u'U‘u) Kn wmhg h Swim umeficgm PM lstkl Ox“ 4<2< <6 C2) 00 n 3 . C13 . . WW X 24’ i Z n 0h¢€fi%€f7 teal” @f;fi;fl$§mfia r55 3 1 ® fl ) WM x :6 'o E W dlmyg 17?: (1) $0) . , ' a a. (9 g [C0 .‘ In/iUUaL 0/ CAYIVCAKBQ/M . y<‘4) he ow- ln: 4 . (10) 7. Evaluate the indefinite integral / 1 +11: 4 (1:1: as apower series and determine its radius of convergence R. 0° 0° 00 ' i 1x :2 E: x" ) ma, .1. : (-x*)":Z<—D“x4” 1’ ":0 1+)t4 hTO mo / _ 00 4 1 n 4h (l Or‘ \X‘4l Sm4x:g(ZO(—HX )d~.x l-Xi n: . w y, 441+. _ _ X __ C +. n}; D m 2 [x|<L (10) 8. Find the Taylor series for f 2 371—1 centered at a = 1. "" (U V” 1. i”) z 2. gm“) (x4) -: H1) + Lei-1&4) + :59! 6(~1)+~~ n! K fl 1. ...
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  • Spring '00
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  • Mathematical Series, recitation instructor, Recitation Time, following series converge, limit mmFar-x‘liggn test

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