Test 2 Spring 2008 Answers

Test 2 Spring 2008 Answers - Section Color: Name tier...

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Unformatted text preview: Section Color: Name tier Style Points g Total Directions: 1. No booka notes or throwing chalk at Chris. You may use a calculator to do routine arithmetic computations. You may not use your Calculator to store notes or formulas. You may not share a calculator with anyone You should show your work, and explain how you arrived at your an— swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. You may not make more than one attempt at a problem. If you make several attempta you must indicate which one you want counted, or you will be penalized. You may leave as soon as you are finished but once you leave the exam, you may not make any changes to your exam. '. 1‘2 points} For the differential equation: (13/ 0 —— = y“ 4: 3: dz); Fill—in the missing numbers in the, chart below and sketch the Slope field for :1): ~23~1,0,1,2 and y : —27~—1,0,1,2 : :5 1—2 —1 0 1 2 E 2 :3 3 “E 5 a '3 1 . i ‘ 1p: <3 1 ‘2; 3 $1 5;. is :5» y o ~‘2 0 g "a ,r “ -1 w 0 n 1 3 f” 41‘ -2 l 2 3. u; 6 \ "““ f 1' (b) Use Euler‘s method with h z 1 to find 9(2) if 3/(0) 2 2 2. 15 points) Find the general solution for the following differential equa— tions. 4 d2 _ 2m) +- la} 0‘33: x3+1 ” l »_ N g“ a»: “4%- 2?” W Y‘l" wal‘lfl‘x =' Mlfifll—m e ‘8 f2 ,\ \/ .*Y\ 1? C {K +5) E ,2; [\g 2: C(‘AMUMEJ {b} 331/ = 23/ ~l—1r300523 1 L c: ‘2 ** ng : KCQSK PCQ-c-L: merxmefl ' x l Pmdx 1, ,3; dx ~1Qm x _ £2 -- Q :: {a :3 4a 1': 7K '3 x u. (15 points) Charles had a lot of trouble coming up with ideas for a mixing tan}; problem for this test, and everything he thought of was extremely stup'nh and the paper shredder was broken so he wanted to destroy his ideas the only other rational way: he filled a bathtub with 20 gallons of sulfuric: acid, let 2 gallons of acid per minute into the tank along with 5 poorly made teets per gallon, and the acid in tho tank (along With the tests) was (lrainm'l at 2 gal/ min. (a) write. a clitl‘erential equation (with initial condition) for how many tests are in the tub. Yéo§=© How many tests are in the tub after 1 hour? ; r -75 (e0) -._ x/ (/ no} If 4“ (10 points) ( Find the general solution of: yW—wk+wy=0 (13) Find the solution of: dW y”+4y:0, y<0):4, P2+Lk=0 aztgw @20 gzl \/ = Cg sic-321% 4: Cel‘Sm 3% \{f :- ~ack Snuabi Jx Qgcl‘COSlX 12 points) Find two polar coordinate representatione for the point Wi‘égh rect— angular coordinates: «1., ~1) Efl L@JH_& E‘gfll) w M.— avg “an (b) Convert the equation 7* = cos {9 + 31116 into rectangular form. {2—- FCGSG’ ‘VFS‘NG” l , Lt: ax +717 air-‘3‘ "‘ H A ‘1 g [fitj’i‘x 46”} l G. 15 points) Find the area of the region outside 7" = 4~¢131n8 and inside 'r z: 8. (Hint: Sketch the graph) 21:“ I f ‘ €W~%€W@ ($9 fax: Co”??? “‘ E “if C) A m. - wwm @E i“%6ma WW2?) cm P ’ j 0 ET? { E” Exams: + §“Cfi35’&@ CM; '2 Qq’fi‘ -—- % 46 l x m CGS®~L1 w w QWW‘“‘%K Q a % 3‘ iHU a: gum? mohwr fly} ,7 I. 16 points) Consider the paaiem'letric curve given by :1; : 2'52 —1— l y z 3253 + 2 \- a (an Find dm. 6)! Z (3):“ UN; 5% (b) Find the equation of the tangent line at t 2 1 ($5259) y~5= étX—?) (C) Find the concavity at i: = l. fifzgtgm“ it 1 OX; 5 Hi \ iéz H (d) Find the area under the curve and above the m-axis for 0 g t 3: 1. t t 1 i A: ji$£3+13tqgcifir y Eatq+9jt dd: 0 a i , f 13t3+%5&:= th%::3; C3 to ‘3 5 sin(a sinm' cos(a + 005(a — tamm' + ,8 FORK/EULA PAGE sin?“ 6 w cos2 6 = 1 tan? 6’ + 1. 2 sec2 9 1 + Got? (9 = (3ch 9 + ,6) -3) sin 62 cos ,8 + cos (y sin {3 sin 0' cos ,6 — cos a sin [3 : cos a cos ,8 — sin a sin : cos a cos ,8 + sin a: sin ,8 tan a: —;— tan 3 V 1 —— tallozt‘dl’lfl , 2 1— cos 2:13 8111 .7; : ——————- 2 2 1+cos 21: cos a: : —————6———~ sin 2:1: : 2 sin :3 cos :5 0 . , cos 2:1: = cos‘ a: — SIDQ x (sin my 2 cos cc (cos x)” — sin 1' (tan :5)’ 2 sec2 373/ = SOC .7: tan :1: (cs0 x)’ z — CS0 a? cot :1: ’ (I (cot 10/: ~ csc‘ a: (835)” : ex 1 ‘1 ~. “V __ (1M; - — :c . 1 arcsm (1;)’ : fig— \/1 — 3:2 1 (arctanzfl’ : 2 ' 1 + a? 1 (arcsec :1‘:}’ = a 2 {L 30 — 1 b r“ 2 d3: S I / ‘ — + ~— (17% V alt alt a / sec 9; d1: S = V’r'2 + (7")? (18 ‘ Mrs") Ln+l ”' 7/71 _’ jflcmn) M) ~ fla) / u l: \ (C) 5) ~ (1 1 b He) 2 L f mm b —- a a in sec [11 + tan a: ,7 1 , sec‘3 3; dx x —2— [sec 11mm 1: + 111 +0 sec 1' + tan z:|]—:—C / csch‘ (142; = 1n ‘CSC :1: ~ cot 317‘ + C 11—122 ...
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Test 2 Spring 2008 Answers - Section Color: Name tier...

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