Math 2214 - Math 2224 Test 3 Form C Spring 2006 Name...

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Unformatted text preview: Math 2224 Test 3 Form C Spring 2006 Name (printed)__ You may not use any notes, text, other people or their work, or electronic devices. Show work on problems other than multiple choice or matching. Use proper units and notation. Be sure series test conditions are met. 1. ( 10 pts.) Find the sum of the convergent series using partial sums test — n n+ "=1 '- L m) i ‘_ J l - fl , _ ,,,..Mu;.,...,o...mmWMNW, UH ‘ ‘ 0M .... Q// 2. ( I5 pts.) Use the definition ofa Taylor Polynomial to find the first four terms ofthe polynomial for f(x) where f(x) = 3:7 and a = l. (Simplify work but do not expand polynomial.) _-, * r > r r ,._—- 2r 5' ‘1’. ( m H_ " 2n 3. (I0 pts.) Use cosx=z( I) x tofind: "=0 A. The first three terms of Ix: cos xa’x not counting the +0. a uni-2 2' : 3‘ rt cosy. _—_—3 flat/Q Hillard“ {E b i _l_ T’Tis‘ “Lies _. - -".-.-rw Hut“!!! w,‘ '-.;-'.‘ :1‘ " jaw ‘ .«aaeagm w ,fil ,. I r . . ,_ I (xi—2)" 4. ( 12 pts.) F 1nd the interval ofconvergcnce and W for Z 3" 2 n “=0 name ofanv test used. I _ POWLI 56w 05 "F" ‘iflafihbt’flcg& ' {\H a“ : (s!— x a“ : g_l-_?:.d)_m, 3%?“ 3”” (M) 1 2 , a w . 2/“ n i W , “Who iégfimmwk‘ Yflwj:h \ 5 3E1-khn1.) 34-;Ztg (mu) R%*€5 ‘ J - L_L; 5. ( 10 pts.) Usc the inte ralt st to s QW cogfiggggqpta/divergence of 2 (MM WY“ r\ ,,7=2n(lnn)2- / 90 ~00 MLW _, r :1": S; 1 [117 W)? WM\ L I EQIWY ‘9 - R\ . \O “A b -;2- ‘ J. : 3 H fig, ,.. b flu—fl!— & Lgflmjsng U“ gamma/2 3M? JV 7 R Z 1. 0.) ' k 1 6/ - Next page. . State the :éthQ‘AW \ ,7 .m- -- a. 3gn2f 6. ( 7 pts.) Use the limit comparison test to Show convergence or divergence of Z ’12:] . q _ ” u=| Q I: “9" Bra: ;: ".5‘ dam? my"; Wiwflq I“ a: 391.7%? he ~cll'sés‘3) E: m i “50-- “i a w ‘ M l ohv /. as 4 7. (5 pts.) Use the divergence (or nth term) test to show convergence or divergence of Z T . uzl 2'” +n l “d l lri in Lm‘lm n ~ w s a ~ rs ~9* ._. 2.. “Hm—W- - i a, ,Q , my (. r .02 . n-=-)a0 n41.“ uvvoo 1 1, in 1 dwag [91/ a Hm O J di lV‘ff/rfiQfi l\‘) 8. (7 pts.) Use the alternating series test to show convergence or divergence of 2(4)" n=l ® am éa>0 l ‘I x .,_L_ .' 7,4}Qcymémcaf, _ 17/ ,W {4 Z k /. Q J— / ‘ ‘ '''' e —' -——~- : -: 0 ® 1 W on if: cal do wages by nth-it genes Multiple Choice: Circle your answer for each question. (4 pts each) Max show work for partial credit. 9. Which ofthe following series is absolutely convergent? no _] H U.) -. I? :. CflhV‘t’ffig’N‘ ‘W (P .‘1 a}. n3 {6’5 Q‘H ti k§h1 v\{]fvfisflfii(; Sxavrll{>£; ,1. .'5 Cl l""€'*‘?l('n ‘ Y\_ . °° 3 . 10. The sum ofthe series IS : ““ u:l / I\ a. 5/2 @1514 Mm d.No sum, it is divergent. Over. A Q 3 7m _ ' ,5 9 (“m-aw“ "' : ""Tfl " Mfr “ A! , 5 . (gs i r 5 5 cle 5in I 1. Which of the following series converge? l. i n:| n a. I and Ill only. b. land 11 only. c. 1 only. 4‘ dwfifc—wl lf‘fillt‘flvmc 5.421%? d . P’ Serra fillvflrfiffi ll 5| Hus gavel/ll only. ff} 1 91—. <3) [11 only. fill» (P ten“ \7 l ) cfir'wc.-:fl€.§ 12. If we estimate the sum of an alternating series by using the sum ofthe first four terms of the series, the absolute value of the fifth term. the absolute value ofthe fourth term. c. the absolute value ofthe third term. théthe error ofthe estimate is less than a l3. The fifth term of the sequence {an} where a" = (—1); is: a.—32/5 b.32/120 ®-4/:5 .10/14 5 r ‘3 t— u a. ..‘__S_ml;,_,- 14. Which of the following is true? to l a- 2—,: n=l is a p series that diverges. ,I/W ’ b. 5" is a geometric series that diverges. u=| 0') l ' ® 2— is a harmonic series that converges. u=l H l/L 33377 4.0 4 (A) g /\ ' retreat ' tance on this test. _ I pledge that I have neither given nor received unauthorized mamb— ...
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Math 2214 - Math 2224 Test 3 Form C Spring 2006 Name...

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