ex1sol-b - MTH 133 —— Section 1-4 — Test One...

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Unformatted text preview: MTH 133 —— Section 1-4 — Test One DEPARTMENT OF MATHEMATICS Michigan State University September 15, 2005 NAME: <3 3 l 5* “Hi7 i”? ID NUMBER: SIGNATURE: SECTION: 1. This exam has 5 pages including this cover. There are 5 questions. 2. Include units in your answers whenever appropriate. 3. You may NOT use your calculator. 4. Sines, cosines, and tangents of simple angles are to be written out. For example, if you have a cos(~:—), you should write 5. Present your solutions to each problem in a clear and orderly fashion. Include enough steps, including diagrams, to permit the grader to follow your method. Your method must justify your answer. PROBLEM POINTS SCORE 1 30 2 15 3 10 L_.___ 4 20 5 25 TOTAL 100 Present your solutions clearly. 2 , 1. (10+10+10 points) Let A be the region in the first quadrant enclosed by the graphs of y 2 M55 + 1, :1: = 1, and the coordinate axes. (a) Draw a picture representing the solid generated by rotating the region A about the az—a'xis; set up but DO NOT EVALUATE all definite integrals needed to find the volume of this solid. é thfir 3 gvtfi \i‘ef‘é’kfiilj {rags 39(43‘3815 {Ring a Z i i 9 r V f '2 gages 9:2le at side Viz ii is??? 1) 53% E5 i F , 7 ' ‘ a k i 2 fikgfig % Z {Rwy/ex: vflm/xé’ sold *3; i {r e 5} 4525‘ i LXLRé \ ';, {fl/‘3 , , 2. {95565} +i) 55>)" i M 3- jfiérfieaffly a (b) Draw a picture representing the solid generated by rotating the region A about the line a: z —1; set up but DO NOT EVALUATE all definite integrals needed to find the volume of this solid. <ii'éé Wi’iwées‘fiilif; {was iéefikng“ wt? Wesiténgg fig?” 0 +0 ’3) Gain” faxfigyg : Q d’ FAKE/f} (Qéirz‘is 7'; j i / TAN/f fagflgg :3 Mei ‘2 ifc’jws )1 K e g ' f," ’2 x i} Z_ A ‘1 a; val. w ggfil‘) » iiéélfdtj «% E(7i(2\zi i?($+rejws)”> )dj’ (0) Set up but DO NOT EVALUATE the volume of a solid with base in the region A and cross sections perpendicular to the m—axis being squares, Present your solutions clearly. 3 2. (15 points) Find the area of the region enclosed by the curves y = sin 93, y = %, and the y-axis. R0? (was skmiad mfiffivx . E e a _* % g I, § Wfifiéfizm . m :2 x 7? 5 t’ “5337:! n 3v 353” 71/ X m “g 3:; 5%; amtfi 1 \ A? f a» v g‘ A )2: I (i x ;\V» , U :\ ti ’3 é’ 3. (10 points) Set up but DO NOT EVALUATE all definite integrals needed to find the length of that part of the graph of y = 2x2 below the line y = 4. of liwké : .t i 1 Leakage-hen“ fig :‘72 Eczé; emw, @15ij fig;- W , r v .. l a ’9— h Weiemfie I j H (4%? 94V- Present your solutions clearly. 4 4. (10+10 points) Suppose the velocity of an object at time t is given by v(t) 2 (t — 1)3. (a) Find the displacement of the object between t = O and t = 3. €th 3 : {fflxx}; 3’ ja'ég “ginggéffi m4} 3 Swag" “Elffi Wit} m} Er Ge {t <; i V{’{>7’0 i(€<§ 6.2g “ $3 {3.19% ééyMQ" 2; ,g M W » mi,» % - G C 4* r a ' ”‘ ’3; ‘r 4 § 1? a i (“t/3‘) :} (“tykyy i we" 5 . r i 11;» 8 {W 67L 3 v i ’ w O :; . 3 ‘% (b) Find the distance traveled by the object between t = O and t z 3. a {Skg‘gn‘ zi‘ ,7i 1 , k , 41 f”: V: 5 g h 4 a? {{y x: W q f Present your solutions clearly. 5 5. (10+5+10 points) A tank of base radius 4 feet and height 10 feet is formed by rotating a portion of the graph of y 3 £322 - 8 about the y~axis (see the picture below). The tank is filled with tapioca pudding of uniform density 60 pounds per cubic foot. The tapioca pudding has gone bad, and all of the pudding must be pumped out of the tank to a height of 2 feet above the top of the tank. y (feet) (a) Find the volume of the pudding. , ‘ N. w i / shape eta? :3 fl f c} egg 3,57} (:54; .4 4‘ [f I” W“ w , (b) Finfithe weiflrt of the pu ding. vy' 6; EL giggly/8 ’ f ’3’? ~33" f‘é) ., 3 t it) j, W? ,‘ 2 i gn’né fité'flSignf 5’5 CéeAS‘l'fiéif; H £%*lb {j j (:3 low; :: Slat/151* » j; "1 a ‘VélW gé‘gé9fl:i§650 35135)“ (c) Find the work needed to move all of the pudding in the tank to a height of 2 feet above the top of the tank. ngflgfi filiéé’ié Agaéféj {3‘ §9m§§r C134???” “flew peg/{ficfmj at}; ‘tibfl/ mm? W «Cedriafaga [New a Sift? 5‘5 Ffig‘flfi’j diva; gaiééim 545% 23533" ca age yam page? {ML 7%?) fig :3" fa??? Mt)“ ./ Wfifk W‘Jéifll’ “(:9 g" 5‘ 4’16 at A225 117’” ' ‘3' “’73 Z36 30win w mama? 42ml VA ‘ “l? 95 jaw 6e 7'? (gave: ‘3 (“2} «a3 511%??? 933 iii vaw‘éé 4w??? +0 353 beams? %‘W 3‘5 W W”? a? be pwgg M 1W éjcm {’0 a. 1% ix? jg be: $7 (fi%‘flé\({}’€j) .: 2: if j: (9%?“ Jr 5%} *Hé’gg? r3 3 €297? “939) ~ 9 l { LL 5‘53 L M}, "‘i c? ‘9’ ] a ’j/zfé 3“ 2432:; if L 4&3] MM ...
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ex1sol-b - MTH 133 —— Section 1-4 — Test One...

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