Test I Key - TEST 1 Math 2250 ' "(1 .1 x,‘ Feb 4,...

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Unformatted text preview: TEST 1 Math 2250 ' "(1 .1 x,‘ Feb 4, 2010 Name: ' ‘ 2 ' by writing my name i swam by t-Ilf‘. honor rode Read all of the following information before starting the exam: 0 No calculators are allowed. a Show all. work= clearly and in order, if you want to get full credit. 0 Do not Simplify your unswor much, or at all. 0 Circle or otherwise indicate your final answers. 0 Good luck! The results will appear on wwwelc‘ugaodu as soon as they are. available. Problem 1. Find the volume of the solid obtained by revolving the region bounded by y a: 1, y 2 1 5 I g 2, around the sit-axis. R; AV: WC \ _. “*2— ;l-" > 50 2 Problem 2. Find the volume of the solid obtained by revolving the region bounded by y2 z a: and y = a: - - 2 around the line 3; z _.1_ ‘33 cj'xlw J \- t‘ on}. SR“: . \ AV "' 2.1a- - 011 i- -' i- R: \I-a-t = 1-H . I.“ 2. Kfl‘ .— {kat — — d fibtd; \IL‘K—z) 3g: .3 = z L'ufig’fc og— t'xkéskq‘ss‘z‘om‘ V‘gufi'h x Y 1*2‘212‘ Y1F1F2:G (\1—2)<\i+2.\.):° 1 3”» T=-"- CAL-A ‘2. 7— “ CY+t j<1+z__\{2\)= “— ‘ z ‘1+\ ‘Efzqu- \J: SQRM ‘1 Q E< ‘ = -'2_~[—t\{1—-13 -l M H 2- W 2.. l 23' ,1 ffl‘ j}- .— L EL .- a :2"QCZ*"”‘W"H "“ é"*"‘\"‘?*3 a a} ‘ 2-4:»; ‘r h] - .— ‘n‘ll' ’_N__ ,_..._ ........... .. I. m--"—'—""—_ 'fl 1 ‘ L— kfi‘wo "We Mag-«me w u Problem 3. Find the length of the curve defined by y = 2333"2 + 1 from a: = U to :1: z $ x. \ ¥0=3= 2x241 Q‘Qq: mix? = 3x: k-t-JQ'QJZ: MN” 2, UL: bk?! iwsfiix.sg AKE%A“ xto 9‘2"“ .. \ge‘ u=K+3= . I; H U—Q L "" _— 8 ..-—I‘ “.1 a; < 3 11!- 5 (e ezfimj—(fiu—zx w)- -.».» 3x-‘r if}; — at?" 5' \ -'- \ , t A” a __ k m f? .I u \ _ t: .‘ '1? g..- 13”, ‘ L 3,4 "r: j {x Am i: J t 2 I '3‘ .4 . L - Problem 4. Set up, but do not compute, the area of the surface obtained by rotating the curve 3,: = sin(21;), 0 5 :r. S fit, around the line y—axis. (Your answer should be a definite integral. You don’t have to evaluate this integral.) " ML- le-A’L R. = v. JR. = H— ,1:ng oh: ._._._._.....__‘jg\‘ T 1=SM(Z*\ A =l-wS x E Hr QGEI A“: o n—-_...._,_ _.._...._ HEM—HE a. r” x 'l ’r\- . "1‘ .. :‘a 1 S a. an; . ,-_!l l\\\‘\\\\:\‘\_\ \x..\ “ SKM('2_‘K¥ 2."? S \ + Ll cos (Zn-‘5) o grée): 2mg<lt3 ‘ 596‘)": RM: (Ear: Wu.- ---- w x "A ’ E" ;,.M“e- Ii 1‘; 'J‘JE'WC‘EBE <m\w1a_§* LL“ @0951. b“? I, Ala-c, A a. 4: . ‘ .. ‘ e. \ ‘ A" “Gar wa._-1 wfl'fnfl'a‘? O 't-Q‘A-a Eur ‘A‘qug a _ V“ " a ‘3’ F a i “h ‘dl‘k ,_I \ \chwC \K‘” 4‘9 3&3 j — 3 gm («17: hi \ K = -_‘______'_______ 23g 2 St“- ‘} 2 A _}_ K ‘E ' 7. 4-3 \ 1—11 \ v F a 5‘44.” +1st v5 UJrou-ué for gang“ ‘3' 3 L'MJEt-f‘ 0. re kwd’! 50 ME” 064.!- __, 5.1, pt If n< ._-?' (:- Eva—'3) Mali-‘9 5’ x ‘h \I 1 -‘ W . 2 h. \ | J T glv aw ‘ = '1;- "'—"' .m—n-f— X L 3 L I UI‘ . \ ‘ — SC“ 3) w 5 f g, V_.n‘._)'4_,.h.g‘ {A I .I .( :5 "if: 0 7L ‘_ ( I4” "- o , _ j 2. _ .r“\ r. A ‘92::- .3 Renal g; ow __ _,,_.,.....a- .4 So) LL-ue ¥.,:-.-3—3.A‘ c “1‘ a, uni... ke- - i 91.; “1.9": if“; r...” 5‘ s. "c 3.9:} a a" a? .1 “ha . ht ._J' .Q.o:1.,r CM— “or q 5 Problem 5. A cup of tea is taken from an even when its temperature is 100°C and placed on a table in a room where the temperature is 20°C. If the temperature. of the cup is 70°C after 5 minutes, what will the temperature will be after 15 minutes? TGBFF—Ts f" Curd-rs 3 9.4“! Hire. '. ‘5 1-.- 10 :fifiokav: C n.w\;1qat \ Am- gmrme “firi- are To 1: ‘00 JEN ih-i: "PW-91‘; 4.3;! “.33” .234? --=‘~"r.--'? q Riki?- _ wSx-a fling. 'R 1 JC== S “TC'bX‘ *0 ‘FOH LO -..-. (mew-29‘). e 80 “-.t' Sc; 3— '5‘: 9 “‘5‘ 3‘3 '5 g -\ E’— xiv—Lux— : --—- ,2. _ ‘- V:- ‘K -- 6 so a 2 s a ‘3 x ,5 Inn‘— A'QJH'” ‘8 “m: ‘(‘S)-~ lo 1': (\OG ~10) E = 30 Q 8 (TOE) : 20 e,“ er“; 3." S 8’ 1 E 6 Problem 6. Solve the diflerential equation = 823’ with the initial condition y(1) = 2. K -15; “Se. hw‘L+LQ\ Cahakt'JFKGh e. .. ._ \ x\+ __ -2. ' M C x-livr-z 8:9 “4% Q = \V‘ L.\. C :_ C > 8's? C ': 7:;- "'2 _'Z_-§ w‘é 7 Problem 7. A tank in the shape of an inverted cone has height 10 and radius 10 meters. It is filled with water Whose density is 1000 kg/m3. Find the work needed to fill the tank up to height of 5 meters. (Remember to multiply your answer by the gravitational constant 5: : 9.8 111/8802.) Do not simplify your answer. 3 gm;- ... M ....... -. ' l0 — w- . _ .JSI'R“ .4. " vakwm 2 11:) r a? R. \o D 3 I“ ‘10 :3 l - ' ' So R=j S w : ~000‘fi'i. '3 0 AN 3‘10; woe—K = Ani'g‘l-a'nge // wigs Ki: \\ z, 3‘ VOL‘U-qe AQHS: \\ Lér‘ \ooo WR-L Glut = 1? 31" 3“] k ‘_ TWA“ V‘ x\ 8-1 k 2% g1 3 \A I. " T 3Mfi_ L. \_I__ (lw = "rrfflifi ‘Ofle‘ih 2, .‘L C ‘ Jz; ‘ 1 g "k; J :r ' a f:q_1_ Luau--F: :3: "iv-14¢: “‘-:"-;’—‘H=~3 m ) 54" “E5”: SR-W-S 80 £vam \I=O 3:5 ...
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This note was uploaded on 02/21/2010 for the course PHYS 1311 taught by Professor Wiegert during the Spring '10 term at University of Georgia Athens.

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Test I Key - TEST 1 Math 2250 ' "(1 .1 x,‘ Feb 4,...

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