MATH118MS00S

MATH118MS00S - University of Waterloo, Waterloo, Ontario...

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Unformatted text preview: University of Waterloo, Waterloo, Ontario Math 118 Midterm Examination Time: 2 Hours Date: June 1i], sees ND CALCULATORS or EITHER AIDS PERMITTED ‘ ' - ‘ - w. {1. Burma-“'19 {Pl-int): {d l LL 1 j, Initials: '~ i 4" i - 'L phi."— iiLr 21.. LD. Number: - f K Section: Signature: - - Instructions 1. PRINT YDUR NAME, ID NLlhiIHEIit1 K SECTIDN and SIGN YDUR NAME [N THE SPACE PRUVIDED ABDVE. For Markers Only _/. 12 LG! 3 3. A complete paper has 9 pages 5 g] including this page. Check that you have a complete paper. 3 q 4. Answers should be written in the spaces provided. If more space is required. use the back of the previous page and indicate where your solution continues. Note that the last page is available for rough work. '2. Indicate your lecture section by checking the appropriate box above. 5. Your grade will be influenced by how clearly you express your ideas and how you organize your solutions. Unticly and,i or illegible solutions will be penalized. r 1. Evaluate the influwing integrals. [3] {a} f aecgmtanamdm I 1 56:31"! MM [£31.11 / KSQQW —seszmg .{ :L , : =§623XJ¢W * §Sc3’+’fiah-W5>< =Efi§»r%wfix+c‘ %h [5] {b} flzflmdm \fifi xzfiiflj 15 gluidulfln—‘r ixilb'h3%i% « "W . J Ham “3'. - lc-‘Ifi" : r :_ !' 3&315'“ LG " “2h : ) xi '5- ?LNQQN “\‘Wamlg NEE UT: 196me 303% 6 WT - Lg 3’ '1 1" 33s”??? lt'bfi’t?) [115353er N ’.‘2—EJ»_\E_ ZSIQQ-nLfiLflfiLE} \lb 3) "l c [63 Uwguffij inflame 10063—9 - CuiPQéQB ; l 6 Him?) 1% «—g 52%me '— [. Ggflé—(r éLuSLQ“):%{-%h$lg 211195294? USEf-fi litus‘i‘fijl ‘11 5 flat} I3] Hint: first find the poxtiol fractions decomposition of the intgrond {b} He the result ofpart {e} to eeeieeee junefee. g (WEN: NM] * 3.5 m M .. D x 9‘ UMJL" l [X‘flx "' S [in 533 iii] I—erejfileuex iMx : fiUan-u Min-x file-x TC, eel)“ 3 l m ms t: n 3. consider the parametric curve at = t2 + t , y = t2 — t. riff-'1) LP \1 [4] [a] Sketch :1: versus t sud y versus t and use these to sketch the curve. Indicate the points wheret= -—1,[}11 en your sketch. - 1 ,,.. L “E nt"-i:*TT -' “t y ‘1 %¥ w lute} —* can) Qlu FR Q s 6 x J x" he! . sushi '01 upi. [2] [h] Find the points where the tangent line to the curve is horizontal or vertical. Indicate these points on your sketch. i ' _‘. 3%,),k it; 111:4. m": 3H / fiH @ a); i’u «gift \m'fiQ * ‘ ‘Squijwfi win?“ is Lulu: ssh“ Wk?“ fl BNEuteflféitfl at Q xii yup,ng has? 5' [deft-ms M 5} ‘“ Li” m fifi‘lqy'fll- Marni M HH‘UI '51— 5 NH l 613009 ~3 - 3, 3 u. v :4} m)» [3] {e} Sjet up1 but do not evaluate, a definite integral fer the length of the portion of thecmefiumt=-1 tut=1. [4] [3] Mathllfi - Midterm Ebmminafinn aplmg AM 4. Consider the curve given in polar co—urdinatee by r2 = 1 — 21:05.9. TM”! a" I": cue. 13 4% {3} Sketch this curve. Delentifj,r on your sketch the points where H = 1n” 2. it, 37532 and r‘ the values 0f 3 where r = [1. T1: 1‘ rQLQ5JO {'7 Kl kit-es?! Mntnun » Mlflliflfln Wummu ulna-Isa -mw u i 5. Consider the sequence {en} defined by: 61:1 , cn+1=cflTH 1 “21‘ [2] {a} Prwe that the sequence is mm. Clci C);- tzh LL79) H qPPmIS waft Stet/'qu :3 r‘ntftasinj “swam Cue-DC; . 6 h w: (*HL7 Cut] («micflii 7nd?) 2 ml Jr 3. ‘1 (“L7 Cm when +17%. Sir-we (flip! 9917C; in“ all In I“7"” rand 4! MVEMQ 16 WithIQ—qixefifimgflmmfi [2] {h} Prove that the sequence is heuuded shove. - figgunuz gmmfifi, L‘) hath-1, ‘ky [0 Wm Lifci<1i3j i-It-A Mm, :H prick) Z r"-.-;';. I'”. Jnueru MfL‘E—gkl K..- (ul 3C1? <3 1&5 {m 1. Z, Lemme whzm (emu. Cqu claw) ..¢n¢,]eJ ml :SERJJIYQ “:5 idem-1M6 have (khaki [3] {e} State e theorem whieh that the sequence has a limit and find this limit. I hut-L I “flail!” I Qmaflq'fltnfix IS lfldfldfimj (lift/d hit-j [fl/l UPPEI ii haj CL [i-Mfl'; infili 5152i Lina L 6" 5.) fl) L “'- LJr 32 .1. - 7/ 2L: LH / i {3] [3] Mathllfi - Mldtrerm mmun Uylula uuuu 6. {a} Find the smnofthe geometric series "i 34 ST '“g- M us 5 .n J h f“ it“- : .L'"L‘_Jo[6_.li.} fi‘flfr-‘i “in 3 'H S 3323 1.5 {13-} Find the sum 08'3": infinite series 2 fl partial sum 5'“, the sum of the first n'terms of the series. Hint: 1 law I”? SK” ——-' 1 n{n + 3} by first finding a. formula. for the LI firm) H ,fL—Lf mag“, 41: LtLil new) :3 6 an n+2» n+3 I'M“; .:_ he; SIR o) l] g '1 H IM r—'.-' a); k / 1 l 1 _ _ I kfik+33 _ 3 i: k+31' 7'. Determine whether the felineng series converge er diverge. giving the names of any tests used. ' m 3 [3] {a} mi 7} l i‘br [OFQQ n I n=1flBfl “11" 'JD'X n 2-2.7 3;. Jan CuflWigtbffl+ :3 Gt 3,“ I my“ “TC wel- i gaming Sum 6 3 Fl"! Mix (Dingle weigfi) {1&6 A; _ 5 Non %e1 abnwatd in)! like Chmpfilfleeq ed, n Kn [3] (b) 2,3113 “=1 [3] ...
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MATH118MS00S - University of Waterloo, Waterloo, Ontario...

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