Exam2_solutions

# Exam2_solutions - SSM 317—01 Engineering Mathematics...

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Unformatted text preview: SSM 317—01 Engineering Mathematics Wednesday, March 12, 2003 Open Book Exam One Hour Examination ‘ Numbe; 2 Answer a_ll questions. Questions have equal weight. If you are taking the course for 2 units= answer only question 1: in 20 minutes. A 341 431 002 Find 'all eigenvalues and correSponding eigenvectors of A. 2. A bug is crawling on the curve C: r = costz' + sintj + :51]: 2» (a) Show that C is on the cylinders?2 + y2 = 1. I L (b) How far has the bug traveled from t = 0 to t = 211'? 1 (c) Find the unit tangent vector E to C at time t = 211-. There is a rainstorm whose velocity at each point is ﬁx, 3;, z) = \$315+ ysj + 231: 1 ((1) Compute f(m,y,z) : v - o. l (e) Compute '2'; in the direction of E at P(1,0, (270%). i (f) What is the maximum rate of change of f at_P? C,U,14‘] ﬁ,(ljd,o“ 74: i" a. ezyi+(m+(2+c)z)j+2yk B. 53"” Let C be the closed triangle going from A1(1,0,0) to Bl(l,2,0) to Cl(l,2,1) and then back to A1(1,0, 0). Compute W = fee. dr. For which values of c is W independent of path? Why? 9’ 3-) I ..-.-. (3 “r\)[(3-A)Cz-,x) - a] - H'L‘M'Z. -r\_) 50—? v-ILROJ ~—¢:JJ '" [3 '7‘) 1le“‘r‘) ~IédZ~U : (2. “I‘M 9 4» HI #6] 71 “(OZ 1‘ 115/ ~7] ”(1 “r0 (A +1) (A o) ZQQ} COSL&*II'h‘—é' =/ I=I> C '3' a H XL+V1:_/ 1? @ EJ 4’6’MV‘W); ./rfr’ elf: J r’=[—sa,&.cem,-§e q. " ”5’3 JIW’LM‘HH -=-. H.915 C9 6,) 0MP: fired pCP)-L1 ' (6*, GHQ-234’ " L4 3/, / =. (/61) 0) 663 T) Jl/ﬁazolé‘gtzwjvﬂ -r;+:i"'" do *0 ,1. ?(7.';y) L) .0 - @ ‘F: MQK Mn a‘ﬂ Oéﬁhafu (3‘ fr], +1":- Q/IF"¢G?“I'¢;” 0‘6 flag gram/I336?" c,”— P 0F 4 in du‘rcoh‘an .910 hadl‘qu?" an‘ [-7 5) Darin. rLr'vc. :— jrad ((#3) *- grad 106/9) ”grad VCCN// " ”st Haw - =._ 614-0234- (6627f)3’2,)l €424; r60: Cl. 315,6) e: /“~>0 an go. 2.11 Vow—=- Cw, / awe, 9%] O . 5‘ ma,» .-. 5: waives m, one =- 53; r 2(9-+¢)¢ae {I [\J [1- 1.. f""\ "€- 9? \1 Ch (J "5‘ Q ; (I Z " (21%).] "J2: 0 ~03 :4- IZZY—(J : 56“?) ‘J(O) + #6:») :1 C_C‘ O .0] :- 5? {£35 (3:0 ”Zia/Agile. Sg/L‘Ilfzbﬂ ”01%: but. are. buor‘ﬁz'hg 0'1 *t‘cv ,0,th ”:05“, *4: X*CoarJ/'na7‘c: d’ﬂ our. runafr‘on idea-J HaquiclcaorL {'21:- l/q/uc. gate #4:. {fl-m. 2"'r""¢<3m=-/t :0 10c 64h I'Sha'fe. I} 9‘"! wart. 014 +1”; y—a ﬂ’cn‘a‘ J 5‘ [(+(Z+¢).3.J 2y] 1 6mm» A; Eér+aéa= 3 aa— M Ma —-—__. 171 9;. <9; ...
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