test1sol - 'Uniyersite d’Qttawa -» "University of...

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Unformatted text preview: 'Uniyersite d’Qttawa -» "University of Ottawa Facuité des sciences Faculty of Science Mathématiques et de statistique Mathematics and Statistics Calculus III for Engineers MAT 2322B - Fall 2011 Midterm I Professor: Catalin Rada Time limit: 80 minutes. Closed books. No calculators. . 51/ 40:: Instructions v [I ID Number: o This exam has 8 pages and you have 80 minutes to complete it. o This is a closed book exam. Furthermore, all calculators, cell phones, pagers or any other electronic or communication devices are forbidden. o Read each question carefully before answering. 0 Questions 1 to 3 are multiple choice questions. These questions are wort ' points each ‘ an no artial mar s are possible. Please circle your answer or eac multiple choice question. 0 Questions 4 to 6 are long answer questions. Questions 4 and 6 are worth 6 marks each, and question 5 is worth 7 marks, so organize your time accordingly. A correct answer requires a full, clearly-written and detailed solution. Answer each question in the space provided, using backs of pages or the extra pages at the end if necessary. 0 Do not unstaple the test. 0 Good luck! Zinc; Edward ski/enur; 1")z'imrro Ki N 6335 Cnmda MAT 23223 - Midterm I 1. If f (:13, y) is a differentiable function such that ‘7 f (1, 2) = only one of the following curves can be the level curve for f through the point (1, 2). Which one? A.y=1+:l: Lama AT {Z-(tj)= 34'7‘ ‘7 ffiz—l =7 fxfll) -‘ ‘ill: 5‘ B-y=1+em”1 Lama“ 7259;“: 3-l~ ewe fj:\ :7fjul2): “*0 2 __ LINK? A7 5 ‘2 __ c O Ey $ 15095) V ’37 £34 :7 fjopi =f Fy=2+(:l:—1)2 ‘LOOV/ 2. 'L g (733): \A 4’43 2. If f(x,y) = m2 — yz, then which of the following numbers corresponds to the global maximum value of f subject to the constraint :32 + 4y2 = 1? A? 9?: >\ V33) (274,43): >‘(Zx) 283» ‘ 5 Miigfi/Q'W gig) Iii) :7} B. — 4 51$ (0) (Of'Ji) C. That global maXimum value does not exist 2: I”? K: 4“ D1 2% 5530 .27 >,,( :7 3:0 wk" *1 <9 (2,0) m (-M ED ) /_ ' (1va Mile”? L? I 'F. 1 ‘. .5! V\ C133 MAT 2322B - Midterm I 3 3. If 2 = f (m,y) and a: = x(u,v), y = y(u,v), which of the following formulas corresponds . . . . 32 to the cham rule for the partlal derlvatlve —7 au' 82 62 Bu 62 D§_§@ .8u—ax6u E§_%@ 'Bu—Byau F@_@@@ &@ 8n ‘ 8m 81; au'+a_y'él (w, y) = my(12 _ 3w _ 4y). Rm» : \Zj —- 6% ~ L62, 5 j (‘2? whimfi f: (>93): \ZX _ 378,? 9 X? 09-: a: (6‘ f3 (‘93; X [ {'2— Ex ~93) $0ch; <£x / 7 : (QQQ‘W 3:10 1 j (6~}X~Zj)éo :1) < m 6 ‘SK ‘1330 (:9 3:0 ‘17, £3 (7%»: Kai -334) :b 5) x: o (5»qu 30‘ (070') ). (Lit/0) 5 3+0 5 Sr Gvgfizjzo‘ ’ [WW KOO 07/ \2_3x.g~350 -, :9 3:3 :3 \(093) E 3 x20 a) 6 v13 9 E X4 0 ¢) (2 -3x~x:):o SO ivmvzj "he a» 6' :3: 6: :1 37X~323 : \ [7, SO. fix 1 \\1 Pg? —ru +y 34/ 5+": / ( 2:14) 2 ‘93 MAT 2322B — Midterm I " 5 5. Find the global maximum and the global minimum of the function f (any) = my on the region , 7 A={(x,y)€lR2|m2+y234}. J) 2/1. m? Ava «Mg L97): w ml gm?“ >4” X gmlréy ‘ (fat—06m MAY? 2. AT ((3/31) “(Ara/“J3 mow/L M/A/ ;—«2 47 (fa-NE)[email protected] MAT 2322B ~ lVIidterm I 6 6. Compute the following double integrals // (x3 + 3my2) dA, for each of the regions R described below: R (a) R is the rectangle O S :c 3 2,0 3 y S 1. b) R is the triangle in the plane with vertices at 0, O , 1,0) and (0,1). ( < H '2, Y Z / fly) :fg I (13 +3X37’) >0))(:f0 4, >033 i O 3 R if X . Z Ll 1 l6 11 :f( +K)o/)<:L+L/O"—E+Z L42 0 3 P L Q4408) ~3>< +X) v/X : f‘ [ fiflX-H) +244“) Eo/x >17 2* a \~.~\ .............. ,./23) 4’1 H3 + 1(4-37<+37‘“7‘ s L, .3 :L \— n x ~_ X ¢JL ~ MAT 2322B - Midterm I (Extra page) IVIAT 2322B - JVIidterm I (Extra page) ...
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This note was uploaded on 11/23/2011 for the course MATH mat2322 taught by Professor Rida during the Spring '11 term at University of Ottawa.

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test1sol - 'Uniyersite d’Qttawa -» "University of...

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