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shorttest2solsscan

shorttest2solsscan - University of Waterloo MATH 237 —...

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Unformatted text preview: University of Waterloo MATH 237 — Calculus 3 Short Test 2 — Winter 2007 Sections 01, 02, 03 Date: March 14, 2007 Time: 5:30 pm. - 6:20pm Duration: 50 minutes NO AIDS PERMITTED NO CALCULATORS ALLOWED Name: golu‘lﬂmj Id. Number: Signature: Instructors: [:1 01 L. Krivodonova 1:1 02 R. Moraru III 03 B. lngalls Instructions: 1. Complete the information section above; indicat— ing your instructor’s name by a check—mark in the appropriate box. FOR EXAMINERS’ USE ONLY 2. Attempt all problems in the space provided. If you require more space, use the reverse side of the pre— vious page. 3. Marks will be deducted for negligently presented work. Your grade will be inﬂuenced by how clearly you express your ideas and by how well you organize your solutions. Justiﬁcation should be provided by referring to deﬁnitions and theorems where appro— priate. 4. This test has 4 pages. 1. Verify that (O, 0) is a critical point of f(:1:, y) = (9:2 + yg) cos(a: + 2y). Is this point a local extremum? We ‘Hv‘l "F1 ‘ 2% (4M [x‘JED ' (*1471h'h" 0‘2“» > E i \ 4M1 1f; = 2? col {X‘LJB ' 2(%1*71)5;h(><413\ Z TLue mt LMLL O J (6,0) ) f0 (0,0) L! a CrAWQJ Polnfk. a: we m4 at“! ' / 1(7m : ZOO! (x4233 ’ 2% Iih(¥+1‘8) " f2"! Ii» (X‘Qa) -(X1+11‘)L35(x+233 £7“) = ’le I5» (X-l‘Zy) —27 m (“27) — 2 (x147‘3w (\$47) , \ 3 £77: 2 (IDS (3442:» L," San (X+2j) ’ ”7 Jim (‘F‘ij :/ -LH (1",(+,)c41(x*1y)/ i \ TL“ {H [0,0)=2) £7 (o,o)=0 ”W 2 I J 7/14 [Janina (1 'Hz‘“ (2' O) \ulnch QI [Mn 'l‘ev's? Z 0?. it'llzn-J’Q. 71‘- ribin+ [6,63 i: a had €x‘(r~¢mv~. ’\ (If U a» Mn‘no‘mv'“) J Page 2 of 4 Since wax! {5 Mom‘anc ‘Far ”K’O we Ca.“ Work Lyn-H‘ ‘Hm Iguana! a{ H3: Azxi'w‘a J SP} {(\$50 ‘: {1+ij and! 5593) = X‘47é, U! 2 2. Find the point(s) furthest from and closest to the origin on the curve 3:5 + y5 = 1. [55k far J's/Aw“ (ﬁnd) 0'; V {:QVj a ’ we {I} 2x "' )61‘5 (L) Zj = 357: (3) Xc-FU‘ : ’ ’5’“ (I) M I'M-t4 X=‘-O g,- XL]: 23' (-91%) (0" 5/?) (vim W #4 Hitohﬁomml ML HifWﬁUaﬂ-‘ZEE Page 3 of 4 New—2:4 pal/d1: (1&0), (0,11) Rattle My (+641, : 31:),(3-11 5)?) =3?» 3. Find the image of the set under the transformation \,Je J Lz-HL " l Page 4 of 4 ...
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shorttest2solsscan - University of Waterloo MATH 237 —...

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