math143 f03 exam review sheet - \4 Math 143 Exam Review...

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Unformatted text preview: \ \4 Math 143 Exam # Review Sheet Instructions: Work out the problems listed below. Please realize that these are no; exactly like the problems that will be on the test. They are examples of the kinds of problems I think are important and I am likely to ask about, but there’s always a chance (and not a bad one) that I ’ll ask them in different ways. Use these problems not only as practice, but as a guide to tell you what kinds of things to study. Don’t forget to look over any old homework, quizzes, and exams you might have. 1) Test these series for absolute convergence or divergence. 'fl "' [ " [ . ; ”(Hi 5 °° 1 [L i V‘ ‘ (4 °° n! (WU ' " —- a) 2—— r‘“ " ~ Wt " b) 2— ----»—»—~— . . ya u fin“: l 10,, in.“ i: . ‘. ,u, ":1” n=0 9 HOW AC ’ / 2) Find the Maclaurin series for the following functions, and determine the radius of convergence for each one. l "" 2 ‘ “l a) 2 2 LL“ 1,! ,4 b) 2(cosx ) (1"?)2 x2 e' r‘ ‘ " z' t. '1 ’ R 3) Find the Taylor series for cos x around at = I: and determine its radius of convergence. i a I l. 92-" t 4) What shape in SR3 is described by the equation x‘ + (y— 2)2 = 9 ? -- l, awhile? ' LC . , , (0,7)”) 7) Find a) The ““6 through (2,0,5) and Parallel to the vectO ELM/3‘ “W V. 1 2 _ 1‘: . ;. T} L- 'J ‘4 b) The plane through the point (1:354) with normal vector (3,1,5) 3(X I) f ILL—‘2“ <~ '7‘ ~ ‘- .0 J c) The point of intersection between (a) and (b). .' ,3 -‘ ‘.I "i F H.- \ Améwf’f" gheef Math 143 Exam # Review Sheet Instructions: Work out the problems listed below. Please realize that these are n_ot exactly like the problems that will be on the test. They are examples of the kinds of problems Ithink are important and I am likely to ask about, but there's always a chance (and not a bad one) that I’ll ask them in different ways. Use these problems not only as practice, but as a guide to tell you what kinds of things to study. Don’t forget to look over any old homework, quizzes, and exams you might have. 1) Test these series for absolute convergence or divergence. no I °° n. l’{e +40 £351— a) 2:? {W‘L Fifi 13) 210» | 1 a n "=1 __t ”_0 (in 1- ‘) l 0 r,‘ - m J. : n lil'i: I'LIAO (511.. _—_ .10“ “H (“Al - in“ 6&5 ”—9” a [ fi+‘( no "' ”-9 M 6-1:» H? ' “—300 9i-flrcd’ L- 4‘1 me Sn” £5 gent/(1:155 l J; Fix/h" in We. wettest ; We 7 7 .. .. .. . . .. to... tié...e._ecsei;cee new 2) Find the Maclaurin series for the following functions, and determine the radius of convergence for each one. _.._- ?» 1 5.. 1-». h K‘der ”:0 i ‘9? l 1 n {2’ ..«\ a." . M L is.” I \ JO — __' - A ~ 13A iuf i’ ,We .el é— / 4:. \ i V9 "= -1 90 M EWL' \ ,5:— e; ——-—, s :2 Z ox : 2. a” ‘L Mann“ ‘ (— ”en \lrt—‘J V- ( «Fan {Mai {Ur/+30: "('1‘ ii’ VIC-H“ 'jA] 'Jd‘i Ci her: Ci/icifljfs ‘, Tier Mailer-5 c'r curIU-F‘ ijC q,- R = fl . , , 3) Find the Taylor series for cos x ar x = wand determme its radlus of convergence ‘ M ' — ' f e c-' .n .. '7 £- ee elite): Coax Her) ~ *l '4‘ P V ‘ ace-w L. r _ T—E’MS n—‘fl n=~ LI“) 5.4x llfii- O «.— 1 s” I Q H t _ 05X LT - A”?- ¥(X)A L m - : ”(+‘L‘. m "n 1‘— ‘? {T7} 6 HA;— n:’b 'i" (A) ' ‘3' I) 1 ’ fifeomi - qJQ‘ifi; ~ ru-‘L ' '.. ft; (gel (/5 Lit-l(: (M) ‘ n LL». (3,“th LT-OO, 5o 1&6 ngl-ES flit/913:5 "‘l i. 7) Find a) The line through (2,0,5) and Parallel to the vector (”1,2,9 \Tvs l“ ”mi of? ’We nuM (Jars. {M (a) ”mt (la). Pdfutma‘t'fl‘c. [row-q S amme‘f'fl‘c {Car/vi W WH"/ ’X= 24: l K-Z: ”j“: 2&5 (IE, (“f/5' 5/. a; rm [3 accrrflf'vz. (2 (C) —1 '2. l b) The plane through the point (1,3,4) with normal vector (3,1,5) "50—1) + 1(yr3‘) +5(e—¢+)'—'O 3x ~3 + y+3 {—52-4‘7-020 3;; 'f 7/ *‘ml 0) The point of intersection between (a) and (b). Sué9+f+bfr€ Th C flaw-M7 e+flb CZ vac {32/25. {4 (0,3 in'f'a 174 e. ELEV-$113351 In (L) “mi Ssh/e: ‘lflcJ-P ”like foafllrfl’t'fiffir‘ i {Jae ¢..'2__l:2/> lv u" ”l! ; L‘l M m/ b “(Vite {qtraMP7L—f‘“ fit“ {~45 "’1 (fl) f0 1' SJ ‘7». + ”j; +6lfi {0J’\~l— v V’ Win-t— F?“ Ila—- (WI- lqflfrgek‘i' {4 i{:‘ ...
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