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# test-1 - MATH 230-01 TEST#1 NAME KE Y Time 50 min d[4 1...

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Unformatted text preview: MATH 230-01 TEST #1 NAME: KE Y Sept 25, 2007 Time: 50 min d [4] 1. Find the distance from (-1, 4, -2) to each of the following: [4] [4] G) e: 1) (a) the xz—plane 0L: |LH = "i’ (b) the y—axis 0L : J¥L4%" = \lc—ilurqy = J 5" 2. The curve y : «sz + 2 in the xy-plane is revolved about the x—axis. Find an equation in entify its center/vertex and simplified form for the resulting surface. Name this Surface and id axis of symmetry. ->Ll.t»'~1’~+—tL = 2. ' m S‘ueruuz, ft '0. k‘a/pubolot'oi, d? :L SLv—Jé Mﬁmé“ at Coimo) out mm cor QWMvM to Lands. 7 qlx2+4y2—9 x _ H I 3. Using proper set notation algebraically describe the domain of f(x, y) 2 Carefully sketch this domain and identify ail the relevant information on your graph. ' ‘4 @mibg , ' Liz/- XLJV‘f‘ilvﬁ 10 . WOW “ﬁtter 2 .‘i <— Mtvws/“ini ﬂ/ WW 0+ 6‘“ I»; - — -— *1 2. 14:0 8 ‘ IL ‘ -:'-l (914.1).3 x J . , Own-E Ljhaqus 31:11 I i f{ (yam [XL—w 1.7.1 Mt x¢o _ ~ ) ‘3, 3 N’TEL ‘fpdx-‘u omrgeiL. 69—... ~ mi - do. my \ {mamas-(123% ﬁre-m Esteem \ ii“ '\ ‘5” YW‘GIKE we 7‘ ' {TVSEMRW mm Wﬂ‘i‘Fﬁ‘. ' Wkﬁfﬁx‘ww’h \ .Wn Wm M». mama we. as WW" Nathan» 3 'n. 2 [5] 4. Find an equation in spherical coordinates for the surface with equation x2 + y2 +22 2 42. ammmmmmwmw mmmsnmmmzmﬁ'mth‘vammI:‘ gas—H rm. am—mxmmmmmm (:i Name this surface and sketch its graph. \fY‘: W L 1 L ‘- f’ fuse 71441th Ame—Hi: Cf 70.7": ”90402725 _ XLMHQb—RlL: Lp-. ,0 .2: e008; “Tl-:2 snort“; i"! a Sp’ﬂerre. WWWL ﬁfE (0)011] Luff faM§ Q“ mmmmma N01533:, £270 1; m c-ngc. (0,0,0) a—aL 619:5 “0 MM? "Whitman; araamwsmﬁi:mw:wawxmm as. ”w ‘W {ﬁﬁ‘ﬁmmmﬁﬁmmsﬁmmmwﬁvgﬁhw [4] 5. Draw a contour map of g : g(x, y) =_ 11106 9y), Showing level curves for functional values equal to -2, 0, 1, 2. Write down an equation in simplified form for each level curve and clearly label the level curves on your graph. (Al—\$15) = 4% law) I 4: (amp V‘v'j c 5'“ ‘ WHQWW. "TL 2?"? .\ A" '9 r- - - . - .- —~. 1 \ “31% RV: newMyqmeWmmumwmtmwi:imsxmwmwmﬁmammﬁx‘mm{maismE-wa‘rmgm 3 WWW“ Law-w: [8] 6. Put the equation of the quadric surface 43:2 + 9y2 — z2 + 36 = 0 into standard form and carefully sketch its graph. Name the surface and give a detailed description of the trace wear . A (- curves parallel to the coordinate planes. identify all intercepts and axes of symmetry, if any. E , . 1 g -LE’TJ—h ﬂt11+ftL=3Q "F+‘~U- wves «w e. Mpg/W5 MW E *ifma i ,LL I. owe (gigoloiaAaLWrcHL%- t 3" ”3:.‘1 +3. t z dame/M . _ i L i L 1, q'l * Lira at t - 1- " 2': ‘2 «Pg: :1. . '51 9}, EL W _ “ma/w) From ‘ "THVSurgrau, ﬁg k'afﬁrlawq- 3’ gL‘r‘L‘B WW 4% (mom) “a mﬁﬁiﬁrmammmﬁaﬁsﬁuﬂmmm mmat‘mm s\ mumsmfo .\\ a ﬂu»: .Xﬁﬁw 4:;El‘, j, Two [39th (Du-9,5163 ’k>cgw2t¢.gi aha” mm at (.010) 4"» #béjk49 ‘_ Na alvam Wv-LS- a“. ﬁmﬁ&meW§Eﬁ§-‘Z\§‘IKW \’ «1‘6 33mm ‘zthWKQCQéRWchW-E mﬁﬁmmnmﬁﬁﬁﬁﬁmﬁsavﬁaﬁmmas [2] 7. A can of soup is 23 cm long, with inside radius of 5 cm and outer radius of 5.05 cm. Describe the solid region representing the metal in the can using cylindrical coordinates. W G— G:i(l',6‘.1‘:)\5.£ r5595, 05.95111", 05%523} ...
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