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# test-2 - MATH 230-01 TEST#2 — PART A NAME KEY DATE Oct 9...

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Unformatted text preview: MATH 230-01 TEST #2 — PART A NAME: KEY DATE: Oct 9, 2007 TIME: 20 MIN Instructions : a No calculator allowed in this part of the exam. 2. Give complete and detailed solutions to all problems. C: 'Use correct math notation and- symbolism. .2 Units must be given in final answers, where applicable. 3 "All cellphones must be turned off and stored out of sight. [3] 1. Given xcos(2yzz)+e’y =22,find —. ‘33 [ 1M°-"(?v‘1”4-') +9.“ -.- 3- (2%) a 3“ [‘SWU‘i‘J—‘ywaﬁ la‘% '3 + aria = a 5%, [3] 1 Q [5] 3. Use The defini’rion of a par’rial derivaTive To determine gu (1,1) given u2+v2:,'u+v>2 T631: U+V>1 Ut-‘HI‘Z. g(u’V)={3—uv,®u+vs2' (HRH! 7 2' h 40 ekulel. L 3 L \ Inn. > 2. {2w 1 ‘ 1-H». \ — bl h ,3 e- _ ' _3“’(‘30 I: tr; % ’ , 3 Nut. m—slhd. i\w'(' s. \qu gLnMn) -3c M) = 1"; mm 1‘ — (swam) ‘ I”; |+zL+L3+l- 1 int-:0“ k. km)" I» kéo I- P» t: h»; zkdrk‘ - Iwi-u Z-lvk,‘ 1-. 2,4,0 = Z. M904: k- k-boi- L ‘ hw‘. sLI+k.n-3U.I\ g In; [3-C\H~\Ci)1-1 = \m’. 3—1-k-‘z k-ao" K kao- K \wo‘ '" "k. .= ‘wvu ”K. __ I‘m —] .._....1 k—)o" 1 ‘- k‘90 " — 2. Carefully skeTch The domain of f(x,y)=w. g, ‘1 % - x+y \ ‘3 ‘- Reﬁw-c: blitz: S‘MM Maﬁa/hi... \\ 1% (MA 1=L - . 1-\ > 0 (M1) _ ___. _ C¢&£ 11‘ X-\>° o—L 1,)0 // _ x‘n Canz'. :L-léo 4*". ‘a.<0 -Q¥j% siLqu‘H “anl .qu (23“!) %_351 +>L J3 a 3.1 3%" [1+ m‘smw‘a] = M'— 3— Mi Sin-(1'1“?) e: = M) 3-3 '1 + Lxg‘sikczgtt) caMW-tlo_ HI x—oxa MOL it.» l|m%:—u . aim-34:0 -) gar-2r. El XL! * nmm<§mﬁﬂsmﬁﬁmiﬁh\wmﬁﬁWT}mmmv‘m‘ﬁmwmmemmwmm&vwmwwmmmmamawwaremnant». am: lE-ls‘i‘a’eﬁw“ \2 MATH 230-01 TEST #2 - PART B NAME: DATE: Cd" 9, 2007 TIME: 40 MIN Instructions : a A calculator is allowed in this part of the exam. a Give complete and detailed solutions to all problems. a Use correct math notation and symbolism. [:1 Units must be given in final answers, where applicable. a All cell phones must be turned off and stored out of ' sight. 1xuw‘mmmmmwwummwammwwmsmmmzmmmxﬁnﬁmﬁmmwmwwm V \Wcm-Ave \Kmmmtcm%WW\$émmmewm «\$3??me an ‘ vﬁmm‘ﬁmwww u - V am mele .x 2 1. EvaluaTe The following limiTs, if They exisT. Q. Ian) xy+x- 3y- 3 luv;— 1L%H)-3(3-H) [4] (0) lim _ (x,y)—>(3—1)x2+y2—6x+2y+10=(‘h‘1l'3un'0 bk“ -bx+q-q +h‘1l'l'V1H'" ) HO .. hm M -Dwn.{- sub gun; -% ,So *‘dtﬂlﬂh—‘b (ml-ah. I) (1'3) +QH} P695:- 0 Al x: 3 1 hale 3-3 )bs-H) =. In»:— .._..— g In; -0 ”s L3\‘ﬂ)—)(,3"l) m 3Q_' @H\‘- 3-5-10.- A’LNS ‘=-‘ '1'»?! WSW Mulf. DAM ﬂ-L'W = ilk-3) c" ‘3‘ . )L—cl.’ xt‘lm (3% ' 11-41) .- = hm LT” = Inc. 0-33“ .4: ‘3. .1 5W3 [1-3)‘+(x-J)" X93 30m) sun->3 L ' )— Rhoq “NT—3 on», «(t/ﬂows pm. .°. In» w we Cum-:L3rnw-H‘ L‘L'lta'h'b 3 b - x y ~ . [1 ()(x’gﬂm W2 Lune W 4-.» 2... 3m! M \ ‘ '— 1; L L \- ”NA. 0 a”: O M 'l y... L1.“ 1.": D.” X +1 (JETS-ﬂex v3 Lmhtom M alto tun PVC-av Guava-'41.. I er/ow iL—‘l— g [ml Him-“(9] 9-1-th - ll W I" Go; (elrm'f'a) L¥|,“')"3LO’O) X +‘1l’ r904. r}- l'en {- = 0-; £03“ 3118(9) = O [2] 2. DeTermine The slope of The TangenT line To The Trace curve of The surface 2 = x2 —-3xy+9 in The ver'Tical plane y = —1 (IT The poinT (1, —1, 13). 3:. = lat—33 . ZXLM—u) LU)- 3b!) = ﬁt" SL319- QW'l-Mfwﬁﬂou, Is 5. \WW‘WT‘WV“;Wwwwﬁmmmk“wmﬁwmmmﬁmmmﬁWﬁmwA—W.\ermwr .mv.nmw.m~.\~,—.\=-“-,.—.—.-.m wwwwmw.uuwﬂﬂﬂm -' Wmﬁaw’mmmumvmmmﬁmﬁ :mmTCs?‘ Via \$1?me SSE [4] [3] [4] 3. Verify Claimuif's Theorem for u(x, y) = sin2(x) cos(y). ' - Q. 6 titty”) .-_- Zsuitxlaoaﬂxicuiq} ‘ “5&a1)-'9'“V*k“‘l'l) uﬁﬁt‘tl'ﬁ': 33 i[2sw(x)m{xlcu(q)] u. —33'“M‘°d*)s'“l‘1\ WM“ 3‘; {—smhmw] 4 - nucximmmm 6 ° . “7&3 (m1) —. LL.“ 59.1) 4. Carefully draw a contour map of f(x, y)- x— ln(y) showing fiv level curves. 4,0 . "" aka-i 5. Given f : f (x y): x” +x]_n(2y)— ' —3, find and simplify: (a) gm, b): L" 4— lam.) aExbl, .1): 2'] 36'1“),- ‘wL‘Luﬂ (b) fy(x,y) .: 13 L40” 4' X '2’" :79 ‘VLL‘JLX + j I ' * J. (c) fyx(x,y) ‘5 E‘ Y {3644)} 3,: flute) F1] 3131n(4+::J-+ i5. 7 :.: l5 3L 3'4 \ibcLl- 3C3“ +- J5 or 13" [glnlﬂ—ELJ +“L (d) Locum-10 \$31“ = '1— '3Fxnbm\=%[£x(*'93]‘\$[31“1+!”‘b'3‘1 3‘3") ~34).- ...
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test-2 - MATH 230-01 TEST#2 — PART A NAME KEY DATE Oct 9...

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