Multivariable Calculus - Exam 3

Multivariable Calculus - Exam 3 - DEPARTMENT OF MATHEMATICS...

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Unformatted text preview: DEPARTMENT OF MATHEMATICS UNITED STATES COAST GUARD ACADEMY Multivariable Calculus (321 1} mm 3 l'i.-:[t:inud:-1:..I Name; 2!] October, 2am: [usuuc Period: INS'J'RUCI1ONS: I_ Work alone. Show ALI. your work. miners without supporting work Will get'no audit. Erase ur truss out any work NOT to be graded. Circle or bust. your final Wren WRITE LEHEI E‘1' an: t 1 5E; GMMMQEEALIY Egg]: EDT m 2. Work in PENCIL only. 3. A. win shall not bring any books or notes Emu the examination mom. Calculators £5 permitted, hnl ma: null be used to do rutllliElinnlignI division, addition: suhmcfiun, logs and Huncntlnh. 4. This unamination «mists of this DDFBI shunt, four oonscculivcly numbered page: and a funnuiu shnel. Page check your examination for uomplelencss bcl'ore begimaing work. Report any discrcpancies to your instructor. 5. Problem weights an: pmvided in the right hand margin nut to each problem. 1 6. DC! HUT LEAVE THE EJLfiMINAT‘IEIIN AREA WITHOUT THE PERMISSION CIF YOUR INSTRUCTOR. I. Givm 2'- fix.}')= ark-coshwxl filmy: i-Iy a: . F'd—. 4 :1 m a: h [1515} WI 0* ms} 2. Ciml: Hr: mm answer: 'I'ht slap: ml“ 111: Iinc tangent to me smfm z = {(3, y} whfifi bald tantalum a: the paint [xwya] is I'oumi using ___.I _ I" 1.1.! h- 1- [In-Yo] xix E I. d. Non: afthe above (4 p15) ‘3. * 3. Thc volume Ufa right cjlcurar cylindnr is V = at r1 h. Appmximalc the change in vflm, by using the total diffemnnl. EN. as the radius is increased from 2 m 2.2 than and III: bright is deemed firm: 3 to 2.? flat. I "'m " {5 P153 Ii. Sand is pouring al “In: rate of d‘n'i'dt = 31': filial: into I1 conical pill: Willi Whirl: "II' = I5 I'II'EII Hi}. When the radius is 3 feet and thc height is 2 reel. Ihl: height is changing 3H1“: ml: dlu'dl — If} mac. Find the. rale II Ich the radius is chanEiT-I'g'fi " _'" ' {9 p15} 5. A. heat seeking pafltcle is boasted at the paint {1, I} on a flat metal plate whee: temperature It a _ Itcril'lttmzrtlizaTtxnrrtl= Ifi-JK’JJF- a. What is the Icmperatuff $112.. I )3 ~ ' {3 mt El. Find the Inn-en :un'l: mugn me panel 14.. I}. [4 Fix] c. Find the gradizhat {2. I}. {5 W} . . . . . - 2 a 1 — :1. Fund the rate ofehmtge m Temperature an the dlmtton of u = —a' +— j u the 1""; J; +- puint (2.. III. _ "FH {5 F's} f e. in what direction will the partiete mmre away from {2. I] so that the temperatme rims most rapidly? Etpress year anew as a unit @301“. t‘. Find me me at which line temperammfii'im rtm-vi'n'g‘firam {‘2;l{ii-lite-:eliltemie:t'r-e-l:rt:&wall""’r ’- '- inpcmfie} i . {5 p53} , ‘I. Given the surface: 3x1 + 133 + 2" = 23 3. Find a vector perpendiculax to this surfac: at The point {21 1. 3}. n. ma nu: aquarium or the plum: tangent to Ihis sulfa: 31111.3]: ' "' W “’ * V115 puts] 8. Locate all wrath: maximal. rel'miv: minima. and saddie pang ifany, forth: surface 2 - 5 + 61: -43r -— 11—33. Juslil‘y your answer. I {10 pts] ...
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Multivariable Calculus - Exam 3 - DEPARTMENT OF MATHEMATICS...

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