Solutions-166E3-S03

Solutions-166E3-S03 - (14 MA 166 EXAM 3 Spring 2003 Page...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (14) MA 166 EXAM 3 Spring 2003 Page 1/4 NAME GRADING K EV STUDENT ID / 16 RECITATION INSTRUCTOR / 34 / 36 RECITATION TIME /100 DIRECTIONS 1. Write your name, student ID number, recitation instructor’s name and recitation time 00 1. in the space provided above. Also write your name at the top of pages 2, 3, and 4. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. . You must show sufficient work to justify all answers. Correct answers with inconsistent work may not be given credit. . Credit for each problem is given in parentheses in the left hand margin. . No books, notes or calculators may be used on this test. Circle the letter of the correct response. (You need not show work for this problem). N PC 00 (a) Which of the following statements are true for any series 21 an? n: 00 00 (I) If 2 an is absolutely convergent, then Zan is convergent. True. "=1 n=1 by theorem 00 DO I (II) If lim lan| : 0, then 2a,, is convergent. Not inte- 91‘ 5; W n—)oo n21 00 § 1 = I, then 2a,, is divergent. Not tf‘le-a- 95 "z. n" n=l an+1 an (III) If lim TL——)OO (I) only B. (I) and (II) only C. (11) only D. (III) only E. none (b) Which of the following series converge? [73 0° (__1)n—1 . (I) ——————, With any 19 > 0. Conugv , b afi‘cmth‘n 712221 np it", ‘9 Side": tag? 00 n2 + 1 . 2‘: 3- (II) 2 m Dtvvtfiv; . Cam‘wunhn r¢$tl mmysm W‘FUA n=l 3!) 77.21 (III) Z Slnng'l’l Canvafizm be?“ it convuvs mairsohteiy. H n: (fin-low E}, l..____‘°l:3“\ win. 2 3;, n;\ A. (I) only B. (II) only C. (III) only .(I)and (III) only E. all [71 00 F0? walem$ 2(4112(6)1M 26:) 200k ,[I'rst’law 3:51:94 1 . 8 I o -‘ O b “Guam ( l (a) Z nann) 1-:— W;,;3~_7 fiat wovk azwcl test Show all necessary work here: Inteoavoi ‘tesi. Lit €00: 0‘ er2,oa) X .x ‘ gin cavdiinwus, (scythe, aural. gem-.mé ,lsr‘ xef2,oa) M £0") = “‘th :a“ 00 f2 511x clx :L‘m St L oLx :Lim )3Qn(£ny)]: t—MM ‘2 “'1'” t-"D @x : 9.0m [Qn(Qm‘t)-£Ma’"2)] =00 on f—o ob @ 1 . . {2 x “xix V, chvorg emf [By the (“'51:me test, the series is ¢£U€Y<éseflt F5) _1 71—1 W (8) (b) n; > n+4 Show all necessary work here: Attevnoiiwca WES» test bn" G _ n+4 (i) b" olecvmfing? Let £(7Q: 6" ><+4- §l(><)— (x+4)e£‘q-; —‘5<V __ x+4-—'2.\< :4-)(® ’ (x-H)" _ 2‘5 (x+4)1' 25‘6”“? §’(x)<o ,me x>4 q¢@ V... b" Cunt. @wflwab {9“ ”>1" h—swo h—roo ”*4 [By the mermaiinl un‘e 3 test, the series is ® Ccmv e vcaen't J @ MA 166 Exam 3 Spring 2003 Name Page 3/4 Justify your answer and show all necessary work here: ‘ 4. an : n $|h(—;‘—) . J- , @ @ t'ma : 21m __.......$‘“(n>=lxm SW = 4. 7&0 h-ovo ‘7"°° 'r'T. x—to x 3‘ mics Uni (Liven-(bend b3 TWW (OY‘ ’(te'gt Pv Ajvwfiemcz.“) [The series is (Lituzrckeri I E 8 3. Find the sum of the series if it is conver ent or write g partial credit. (a) 2%: :ZLZ‘ (’21—) :: i— (1 +(—£;) +(—i)1-+-n) “divergent” in the box. No ":1 h:| metTDL ‘3: 1. = _1—__ cfiinew'es " 4 4,62%) 5 3;" ] D4 °° (—4)"~1 \ 0° 4 h-I b r: — -— _ ”Z3. 3. a ( 2 %Mmct‘(\b dive-7W 52mm. sen‘es l” a] > 1 i (U U “bat J El 1 n 1 (8) 4. Consider the series 2+. 71:1”! (a) Write out the first five terms of the series. “1 Pt for only fine. wrung ham 1 " '-—2—. +33% — 3"“ 4—in— 75—! M9! 6" (4' all 93'“ Yeucrid, 1 " I '" 3; " £1 + feta” / (b) Find the smallest number of terms that we need to add in order to estimate the 1 sum of the series with error < —-——. @NPC 3 terms 112?] 213')” , (10) 5 Determine whether the series Z( 13 absolutely convergent, conditionally con— ergent, or divergent. You must :jlustify your answer. Absolutely (mm/ex 3on1? use «113:: test Show“ or not 53')“ MN Y}, ® @ {m lied; \ 0‘1"“) I __?_____:-;|Z\1: I: @ >0 < 1 w" h, OFT/I) +4? Froblam i ounqu-Q/r (n box V3 "5+0r3“ n+1 “—wo ”ban-Ohtlofldjv mn«4y%ehf“dw :AlV¢-V'Wu 5 PD, {Av- path». 1}. work m all Lowest mmoL OHSW In baa! miconvcrtbcun't“ Sign 1‘1) “-O't ‘ - ~ SQN. U) (Lloa MIMI, The series is abSol uiel 7 mnV¢v%ent {El MA 166 Exam 3 Spring 2003 Name Page 4/4 (16) 6. For the power series Z(—1)”n4nx”, find the following, showing all work. n21 (a) The radius of convergence R. Roi-4:0 te J y,“ n+1 n+1 @ { 0w”.1 I ('1) ("+94 X 2: it! 4 (xl -———-; 4le am (—1)" n 4‘" x“ “ 3, when Cam/“”361” (f 4lxl<i 0v -\Xl< 1 (10) 7. ( a) Find the power series representation of — 00 __‘.-—- ‘2- 1 .L s-x *5 1- 5 _ a: (about a = 0). If answcf in (a) l‘ ' c . . . M‘s a". / a‘ W" V. certaln value of the constant of integration C' “LLVORV‘IM of 00 Sign errov/ $434. £fl<5-X) = __ fig) wan wnsifi-cwty (10) 8. Find the Taylor series for f (cc) 2 % centered at a = . '2, 1 (12 -2)4"' 900: Z 5‘12) (252)“ zfifl + £1.56”) + ‘ (x '2 ‘ ":0 h'l Ro/ 91:_i_:_..é:—————-T:}. 1x—[email protected] £09: ;-—x'1 «2322-1 x '2. MW?) 3» “-5 £00): -1 X'2 *0?” :—- 2.2 __ L i (_ 5:2 n , _ -3 — A __ 5(3)!) 21.2 X 3 gab): 2 2 4 zmh’o h n “”00 =-'-2-3""’ 5%) =3! 2‘ Z Eo-("fiéaa—z) ' ~ ' ' ,; ~(n+l) , m 560%27 4“) "a 2 5% % ,_,. “x 1;: Z (“Owl”)! 24nH)/x —‘Z)" 2 L19) X ”=0 n1 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern