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MA241_test_2_soln

# MA241_test_2_soln - (When you are ﬁnished fold the L051...

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Unformatted text preview: (When you are ﬁnished, fold the L051. over vertically and write your name on the back) h‘IAQll—Om, Fall 2008 Test. '2 Deditmzml (:a.luul;11.l:m'5 which am not (:Ltpulﬁllu of synlhulhr [manipulation are allowed (1.0., [ID cell phones. PDA‘S, l21.1:;tc::1'13. 01' leSH‘s or TLQTS or UtjlllV'Ellt‘lilf). Nu notes “1' aid}; are allowed. You must Show all work and sufﬁciently justify all steps in order to rec 1: credit for a prul‘ﬂeull Answer (1Ll€.‘tilll0115 1'11 El]? space lll'UVlﬁlOLl if 1::(3531'1’1le; yam may (:0111Jll‘lllﬁ‘ your work mm the back of the. page if tll‘.(‘(l(‘.('l. but clearly luclicmw which i.u'0hlem the. work {'01: 1. {1‘2 [ma az'Lch, ‘24 pts. total) In each part. set up the. integral 110 [int] the volume of the solid of revolution gm‘mruliing lily rotating the regiml bomwded by The graph of y = 7.392 + -=l.'1: — 2 and the line 9/ : l alum“. ill“: glwm line. Before setting up ill“: .i.I111(-1g1'u.]. graph the region, sketch the solid, and indicate which method you are using. Yum do not need to Walllalc tho integral. {3.) The line :L‘ : — l. l ‘ l — ' - f ’ v .. ' - r "v" : r I“ ’ l 'l ‘- f \ . ' k’+u' f x'f‘ A J I (hi) The! line 9/ : -'l. f... , . a \ In! '| ? 7‘ 1 ‘2 I I g __ ll / ’ 1/ : '5 {‘4' I} — ‘1‘ ' * “ ' I --' -_ I , .' I -? \ . J- , ‘ I F ; l r ’ h r "f\ L \’ I J J I . ‘ I ‘ ‘ \c '1 r I: i . l ,4. ' ‘ .,-‘ l r l " L 2. ((3 pm. each, 1'2 pte. total) Given ﬂag} : 432:2 + — 5, ﬁnd the following: (a) The average value of f [Leu‘ fa“) 0n the interval [0, 5]. g -T 'r " ". . l r ’5’ . / '7 F 7 f (fl/3: Dr'— {Z’ I”) I ' C;- " i ‘ 2 if? (h) c such that ﬁe) : fWE .. ,’ﬁr.'ll'- ,ﬁ ' ' 2) ';_‘F‘+U’1Lj::ﬂl j) _ _ U uric/3 _ ifl"-—T_,\II-‘“7 _ - "f : J 'rj} ’ = ' I”; z 2, C — J— ' P‘—'_ ,, 3 v 7 r? H) 5 , ,. . 3. (8 pts. each, 16 pts. total) Be sure to show all work for the following problems. (a) Determine whether 3; : 31cm" is a solution to the DE y” 7 4y —1— sly : O. :J I ' + w x ‘ . p , x “L 1'? r r : ,X " 7L .4 .—,_” + “.1 ‘ "' "" " '7 . _ -' -'.‘ I ' i '5" ’— l :‘ ‘_.--’j r'.’ _ "\7L #:3/ _’ 7 l ‘i ‘7 , ‘ ._. / x: ; u r _ _ I" I} I}; f. " \ I; a' ‘r' r , , ’ ’ ' . C" 5 A? :3,’ v ,. :4 ’ f; 55-" (b) Determine Whether 3; : 3:1"3 + ‘3. is :1 solution to the IVP my’ h 239 : 4‘ 51(1) : p K , ﬂ ,- {'3 l ' ’1‘ | »| _ v 4 , r J 7 “I I if If“ F A K I, J }_ e [a >/ ’ ‘1. l ; _ ‘ _ i i f —* :4 V r? » ,z a e —a a v". 1 f [O -i. pm. each, 9 pts. total} Given the direction ﬁeld ofaume DE below, sketch the solutions corresponding to the following initial conditions: (a) M0) = 4 (b) W3) 2 0 (Cl 11(0) 2 —3 5. (3 pts.) Find the constant solutions of the DE 31’ = ya — yg —12y- ('3. {12 pts. each, 2—1 pts. total} For eneh of the [ellowing problems, 0 draw piLrturL‘: of the eitlmtimi (pal-I: (a) only). 0 Add a. (:001‘t‘linatL—i system to your picture 01‘ the one given, indicating where everything is with respect to that. ('2L)CI1‘Ellll‘c'L'f.t‘ system. a then set up the integral 1.0 [ind work or force and explain what each part of the integral means / rep resents. You do not need to evaluate the integrals! (:1) A rectangular tank 4 ft long, 5 ft wide, and 3 ft. deep is filled with oil having density 50 lbfft'l. F'nd the work done in. pinnping gnv third of the oil out of the top of tank. . i . LA ‘ e r f. I SJ . I. r . : f I: ' f x ,' i " e I '— l ,i ii , i ( 7 l4 1 W I ’I u I ‘ - ,1» (h) A trapezeid-shztped plate is suhniergecl in. water as shown below. Find the hydrostatic: force agaii‘iet the plate. (Note: the density of water is 1000 kg/In'3). V) 7. (1'3 [3115.) Given the. IVP y’ : «‘21:? + 1113-“, gm] = 0 use Euler’s Method with h : 0.4 tu 2'1])])1‘OXiIIl'rlI-E yﬂﬁl lay ﬁlling in the table below. Round Lu 4 cleuinml placus. Circle your ﬁnal answer. HT 11‘” l— ‘31“ . , . f .41 3 I? /‘ L3 ._ Agni—.1"; all“ Ll) 1L6 I, 4, (Z) / x I j ' l ‘z‘wﬁ‘vdhm 4 / I 2* £2 3 + .2». w 9.2%)” .L it Q) “glam W ,1!» , i , a ' , 2 _, , ’4’ p , :2 Mw<¢w “01:91) f6.’i.§:3w¢?. “ (fa?wa Bonus (Spts) C'on‘qdlotely evaluate one of the Four i1’1l’.eg1‘e1]s from problems 1 and 6. Your answer must. be. exact (Lew no decimal 01' calculator appruxlnmtiousl. fﬁﬁ!) 7T WIN" Me I ail-U: ) 5‘63th f ., (Era: (1 ma 5 (max 25%? ...
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MA241_test_2_soln - (When you are ﬁnished fold the L051...

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