{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math 2214

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

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

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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— ...
View Full Document

{[ snackBarMessage ]}