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# test1sol - MAT 1322A W2009 Wednesday Feb 4th 8:30—9:50...

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Unformatted text preview: @ MAT 1322A W2009 Wednesday, Feb. 4th 8:30—9:50 Prof. Desjardins MIDTERM TEST 1 Max=20 Student Number: OTime: 80 min. 0 Only basic scientiﬁc calculators are permitted (non—graphing, non-programmable, no integration or differentiation capabilities). Notes or books are not permitted. 0 Work all problems in the space provided. Use the backs of the pages for rough work if necessary. Do not use any other paper. 0 Write only in non-erasable ink (ball-point or pen), not in pencil. Cross out, if necessary, but do not erase or overwrite. o The problems require complete and clearly presented solutions and carry part marks if there is substantial correct work towards the solution. 0 There are ﬁve questions worth four marks each. ® 5 . . 2 . . . 1. (a) Cons1der the lutegral / (33—3— dm. Does it converge or d1verge? If it con- 0 _ )4/3 verges, give its value. 5 . - 5 f 0? 6/1 = J , 5/1 + 0?. 0/9: 0 (7013) W3 ‘ ~ VI} 3 . =‘/(3 0 (25-3) _ (1,3) 3 I: f . a? / dx = Im/ / _ O? 4/2: a (JO-.3)” £93" 6' [7L~3)% 2 CX3 2 _ (b) Determine if the integral / ﬂ 2 + z d2: converges or diverges. Justify your claim. 1 x e M/ xa 4/1/4444 fé (many; 2. What is the area of the region bounded by the curves y = 4 — 172 and y : 3w ? @ , 3. Find the volume of the solid obtained when the region bounded by y = 1/15, 3; = 0, m z 1 and a: = 2 is rotated around the line y = 2. Include a sketch of the region and a typical cross-section of the solid in your solution. CHIS}- Jail/O}! Ar <21 odaJ’éf 0r I‘lp/j' .4; 5/ 71% lid/16f a); I} 0-,, z :2 ~ 9)! J76. auJé/ heal/(tar [f PM : 9’) - 17 H ‘ 2 J}; m JCT/uh": N V: anIc/x I 2 ® 4. A heavy rope of length 15 m has a density of 1.2 kg/m and is hanging over the edge of a tall building. How much work is done pulling the rope to the top of the building? The acceleration of gravity is g = 9.8 m/s2. Deﬁne clearly all the variables that enter into your solution and provide a drawing which shows their meaning. 1 ca ”3/” M pm Mr Wm M m gaze/I ﬁe?” 5““ W” ”5’ A1 1‘; W wag/1;! é;ﬂ){9f)4x ’U : ”‘76/11 N ﬂit [1:306 0.2L JKL‘M’) Z,“ 11an /%€ flZé 47F % M77 awe a Mir/7g”, w Jim] ya 7% war-4 ff W!” = [/LK'JPGAX— 'J n m 79H (.0sz I‘J’ £1} 5: 2U}; :. 2 (L791; A)! j ‘3’ L =I 7&4. [Ki/WU} a0 4.2—; 0 0,- 14 .9 00 A, M Al= [Mien/z = Swazi/0”” 5. Solve the following differential equations: dy_2:1: (a) (-772 + 1)dx y2 (b) ﬁ- ”“3 dsc _ cos y MAT 1322A W2009. Wednesday, Feb. 4th 8:30—9:50 Prof. Desjardins MIDTERM TEST 1 Max=20 52¢ Mgr/Vin x4 74’ We‘re M14 Student Number: oTime: 80 min. 0 Only basic scientiﬁc calculators are permitted (non-graphing, non-programmable, no integration or differentiation capabilities). Notes or books are not permitted. 0 Work all problems in the space provided. Use the backs of the pages for rough work if necessary. Do not use any other paper. 0 Write only in non—erasable ink (ball-point or pen), not in pencil. Cross out, if necessary, but do not erase or overwrite. o The problems require complete and clearly presented solutions and carry part marks if there is substantial correct work towards the solution. 0 There are ﬁve questions worth four marks each. @ 4 3 1. (a) Consider the integral / Wdas. Does it converge or diverge? If it con- 0 _ verges, give its value. v ‘9 2’ q 3 9 06¢ : / all + f 1 ‘ 4/76 a (x -2)"/~3 o (252)” .2 (2:- W3 2 3 . ,9 0/ Z (75270 CA : jw / (2:4)?” )6 °° 1+sin2x b Dt ' 'fth 't 1 () e erminei em egra /1 m3+ex dd; converges or diverges. Justify your claim. 57nd /+J‘/73772z S Q 3 (25.3! 23‘6’1) )Z‘ ./+Jvi«‘>a 4 9 < .2. 27%" 1+6 00 ﬂ 2 oo . 51) / M 0/9: C :3 6/" Vllrc/ (meager / 3 n 2 ’ '2 4e I 2. What is the area of the region bounded by the curves y = 0:2 and y = a: + 2 ? : (3’ (3)2 9(a) - 31(9)?) - (lg/.01 awr- 5403} = ('2+°'-§)-(3‘1—2+:;> : ~§ —' -’ (a 3 3+2 '3‘ : \$441 1 3 2 S“‘/3 3. Find the volume of the solid obtained when the region bounded by y = 1/22, 3/ = 0, a; = 1 and x = 2 is rotated around the line y = —1 . Include a sketch of the region and a typical cross—section of the solid in your solution. 7A A:l/" I (y >x [/‘Jﬂ‘— “(ﬂ/IQ a we war/Len @ (Q 4. A heavy rope of length 12 in has a density of 1.5 kg/m and is hanging over the edge of a tall building. How much work is done pulling the rope to the top of the building? The acceleration of gravity is g = 9.8 m/s2. Deﬁne clearly all the variables that enter into your solution and provide a drawing which shows their meaning. ”/ng 70 W 4),, 44:4" WW ().§)(7—d"‘)4x AJ '= N57 M M AmoééaWZ/m 9; a}; = /‘£7x,~‘/Jx J h w; = :2 H.790” J’ 1—! 7%“ ,4k/ A} a): H‘N‘: 5. Solve the following differential equations: 4x (a) (x2 + 1);:- = 92 — V1 4% 22+! k y3 : QA[22%/)+C ﬂan 5,5,1 : (bi/210+ Cy; dy 330033: (b) E - cos y ijﬂ 4/; 3 760247 (AC (740 = Ctr/\$41 +a’2m + C To ﬂ : Kira/i1 {kl/112+ (22.1% 1L C ) ...
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test1sol - MAT 1322A W2009 Wednesday Feb 4th 8:30—9:50...

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