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Test2KeyYellow - MATH 251, Fa11.2'006. RAICH EXAM 2 -...

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Unformatted text preview: MATH 251, Fa11.2'006. RAICH EXAM 2 - VERSION B Name (printed): Section #: “On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.” 1 ‘ M ‘ Signature: UIN: DIRECTIONS: I. The use of a calculator, laptop or computer is prohibited. 2. Please present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your final answer. You will be graded on the final answer and the quality and correctness of the work leading up to it. 3. There are questions on BOTH SIDES of the paper. Please be aware of this. DO NOT WRITE BELOW! lDisputes about grades on this exam must be handled the day the exam is handed back and must be discussed before you leave the room. If the exam leaves the room, it will not be re—evaluated (except for possible adding mistakes). 1. (a) (5 pts) Let p(a:,y) = 1. The mass of the lamina that occupies the region inside the circle 3:2 + y2 : 2y and outside the circle :22 + y2 = 1 is: 271' Ea) — -3— (I: Rfsixfla rl\ (cm—7i ‘ Flame 05%” ”" .BgsMQ‘vi ez-‘Vle,5me 5W. Ashe Sm ii: 8 \ r We - \ig L\$\re~\ (ie “it \ Wu . sub 2 1— 10mm —\ 0&9 W “M i i. - 5m "QM 1 1 \e k \ m t .L SE B _, T‘ B ': E E Blot a Mo" 2 3*”; (b) (5 pts) The Jacobian of the transformation a; = 1L2 + 122, y : uv — v is: (a) —u% —— uv3 (b) —u% + 11/03 V M,» (c>—2u ~ 2v2 9”“ ‘- \2m \ M’ffl (d)—2u + 2112 ‘ (e) none of the above. aku\\)\ RV U \ f” 2‘. (20 pts) An aquarium with a volume of 24 cubic meters has a slate base and glass sides. If slate costs 6 times as much as glass, find the dimensions of the aquarium that minimize the cost of the materials. +1 \}‘- W2 =2"\ PERM : { V X m%(¥\\j,Z\ 12<YE’ X2901) \I CUM: (M +in 7'7”; m. 1% *:::‘<:V*7%s effigai at“ CD 1 n a? V Y2 ‘7 M "V" i \I 5t 7 m 6X+122>0k2 $7 QXYFkQV'Z: XXV? Q) %<~.CN \ L333» ) V: 3% ' 11x»?qu XXV ‘ =7 15¢qu- Xxy? 12%) 5C (Mafia) 1 ®—®+® meme ._ 1 6X- L33 I ex: '33 mm -. 2L» Hx2-2L\,\ My?“ by V1 WQX \Vr/xzz‘l'ax v2: ex ’ 3 LL? xzzsxy x23” GW‘ 7 ,_ M: y; 2‘4“: x=y -— _ 2g: W3 :33 Livy ,MW +1 Vl‘l v V ‘3 H xiv? _ 3 ' ,7 (3X :LW ya, o\L X}; l ,. “we 2" Wit. * V a-ZC __ am _ (7 a)? » \ \7 O , \170, e \1 3 ‘c l WY}. 0 y l 3. (a) (8 pts) Using rectangular coordinates, set up the triple integral which represents the mass of the object with density p(:c, y, z) 2 1 + x + y2 + 23 that is bounded by the cylinder 2:2 + 3/2 = and the planes y = z, y = 0, and z : 0. DO NOT EVALUATE. \txhfiéf dz (it ()‘x O Of 3 I m1 Y “er11? die W M 0 film!" 0 ' I 4’1 ear/M u) "m 3 X +\ max/1+? elk -\"\ voluwt 2M- 0”! “" 00"” ‘ orb/r (b) (7 pts) Repeat part (a) using cylindrical coordinates. DO NOT “EVALUATE THE INTE— .» ' .GRAL. ‘ ' ‘W 9% vsmg SO , \ 8 \+v@se+t“slv\‘e¥£dz thdlé 0 MM "WA WV 3 fSlKQ *5. “‘“fi5 3 8 Dr (ZOOS9Ar (EQWLB * (is dz 6U OK; 0 o I 0 2 W W 4. (a) (15pts) Evaluate 2 zmdzdmdy Aim/o 1‘ Th?“- CL- Es Wily" ~ ,- : X \ MW”? 925'“? ck? 619% 21L. H~>8~w ’ \v/ 0 0 ‘ o m + (o '21: I? J???“ : “)1” 1 B x g 2 r‘+2‘d2- (“MA-I9 43”? +5 8 S —%<)5 90$ngde *3 o 0 0 F 0 lo 11 z '1 '-\~r‘*v o “71 :8 0 é- ((11,?) \0 (Amie : g Co$¢€m¢c9¢ u: 2 H 0 =—‘~ Srkrlm- ‘ ‘- r (3 de—D 32 m B 3 +3 : I S o 0 5 0 Zn Z : l3 8 3?? r (A Male _ ’ —5— (imskflfiwsfl Uh: Lin , :ig <3,i_%3-&E 7’ 510- 5 ' \0, = 3—1— Rfl 11%) = '32 “5‘ +3 5. (a) (5 pts) Change (12,7r, 5) from cylindrical to spherical coordinates. a ()2: (a 21 5qu yrs” . , (Bil, mle - SYMZ ., K of o P? D: \BSW (Z: arcsml‘zlx‘sls ‘ KP) TM OJ: 5M3) z=9cOsg 5= \Ewsgz '1 +1 +\ *2 f? = WM? " Z‘OV 6“ Tim/M1 (c) (lepts) Find the area of one loop of the equation in part m 3mm W S \ (dude Jig thfilmdw W “w. 0 flag «L1 , = \+w%L%\&9 ' “4qu “m 14 9 + fismwax M 3 ’ ‘1 9 T at: * 0 + E ~03 = 3:: +1 ...
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This note was uploaded on 07/22/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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Test2KeyYellow - MATH 251, Fa11.2'006. RAICH EXAM 2 -...

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