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# Key_Quizzes - #1 Name Solve the foliowing problems Show the...

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Unformatted text preview: #1 Name Solve the foliowing problems. Show the whole work. The maximai score is 10 pts. 1. (4 pts) Determine whether the line with parametric equation cc u 1 + L, y z 2 — t, z : 3t is paraliei to the line :L' 2 — 3, y :22: it + 23, z : 4 "in 3. WW WW 7% W M is ﬂ=<4 4 §> WWW r—«ir—m 06mm? 4; 50 W§e AM; are A/a/i/ Mira/é / (ii/>1?) 2. (6pm) Find the equation of the plane that passes through the point 130(1, 6, ~4) and contains theline (13:2 1 +2t, y:2—3t, 2::3—t. We fate 2v}; awe/mi £74 71/ ' POW/’4) W {9 Meg; eta-o ﬁM’ %/ 50/2 2/5) ea? We ﬂew W 1335024» (aft) Wm We MW pW M is; 7&7? ﬁx? 215/4 arm .1. 797%?me ”Tr-*7“? Name ...'- Solve the following problems. Show the whole work. The maximal score is 10 pte. 1. (#pts) Show that the point P(1, 1,1) is on the curve given by the vector function r(t) : (13,19,113). Find a parametric equation of the tangent line to this curve at the point P. [557794137 {2/ Me Ow”??(4):<4 7 4) :7 P014) [/69 AYE/(rt) :<4 24- 31:1) to a 742W 7W ,. 7m g5)“; 44 +71 fer?) We "' W07244 2,3a7‘1m M as ”MW “£45442? 7% 474%044 M46. Dan/Maﬁa 7447411374 “7%”? ﬂY 77304 4,7) .§:<4)273>45” 2. (6 pts) Find the curvature of the curve given by r( t) :: (sint, cost sin t). F/(T): (0075/ ”\$1711? 607%). [IT/(19);? ”3ng maﬁa); \$7474): ("Shot GDZL ﬂ”§r74t> [VI/frﬂ; W """""" see) a Beam} ,7 17’76015 W751 owe/7 ”tK / 7 ~ I ——=?/ l K— j WK Rm low 445+ ﬂat 4:: L/gmﬂﬁviv (WW 3741” ant” 4L, J +% gnzfvso 2% @439 t ”" 7 is; ..’? 0V4? [T/‘(Y 7/ 4: Mi 5 at C“ a; 0435: E2) Solve the following problems. Show the whole work. The total score is 10 pts. . 8m2y2 l. (5 pts) Show that. the limit does not exist 11m 4 (w: y)~*(0 0) 9? ’1”? J4 Ill/e? 0/1/40” 47/1/19 JAE/a] 15/; may //««1;1’3191/w>5w% 41W (Mg/E/vC/WE ”23/11/243; :7 R! (X 15>) “-7 (0 L?) 7/123 17) w (ii? 2,: 0 ms?- 01 MAIN x ”7 Li I (Xﬂg *‘r‘ (0/!) ﬂ)x>;‘é 3X“ - 13:" m- 13:: 4_.—.> 42:11“ 0 7L L’ W ,1 ' ”7751; E) 8/1, 1/271 E‘iif's M/ EA/3537L 2 :? x :x" (4% ‘2. (§ pts)D1aw the level cmves (1ememb01 these me cu1ves in the mymplane) of the function f(x,y) rm— my co1zeSponding to z :2 0, z _ -1 and z m 4 Soive the following problem. Show the whole work. The total score is 10 pts. 1. (5 pts) Find the equation of the tangent plane to the surface z x111 at the point P(—1,3,0). ”5g; ‘ ' if”; A 2:12 + y ‘ :5in AW? 5? ﬂ?" Marti/4 ﬂy” 51 “7/8”? :HZZML f/MMJX 74 9 37599) M [WWW (Kiwis; % emiﬁw 2, A w '> 213 mg: "“5 “i “0 ”W W * ”WM/ﬂ) H 2. (5 pts) Using implicit diffeiention ﬁnd zx and zy fiom the equation way +— yz + 263’ m 0. Viiﬂfuafw/tfzwd" J’fwg fate/1, 74:75 NE” CH?“ MK 9. 9 +3 Solve the following problem. Show the whole work. The total score is 10 pts. 1 F01 the function f (a 3;): (2:3— 2: 2)(2y —y2) ﬁnd all critical points and classify them by using the second dexivative test as local maximum, local minimum, 01' saddle point and compute these values. é @ 2x>(27”71)”0 140/) be ﬂ] (2x—->?)(22g):-0 mﬁM/WW 9/ >9pé2~9>vo Eﬂj .2.(%.X>(,.y)w w M W2 1x7 2» (2 —~ 2x)(Z—-27) :— 4(MQﬂﬁ) Solve the following problems by the iteratccl integral method. Show the whole work. The total score is 10 pts. 1. (5 pts) Calculate the integral of f (any) .1" +2 3/ oven the lectangle R — {( m y) : O < a: < amﬂwwflwllwf 2. Find the volume of the solid lying under the elliptic paraboloid 132/4 + 112/944 3 1 and above therect‘rmgk §={(m. y): miga:gl, —25y\$2}. 6““, x2. 32‘ Hun..." l C» Solve the following two problem for 5 pts each. Show the whoie work. I. In the double integral ff 4y3dA the region I) is bounded by y :2 a: —- 6 and y? = :3. Sketch D the region of integration and write the integral as an iterated integral. DO NOT evaluate 2 Sketch the 1egion D inside the circle r H 451110 and outside the ciicie r - 2 WIILG down the 1nteg1 a1 [/0 f (1,1)dA as an iterated integraLusing rPOLAR eomdmatos ‘‘‘‘‘‘ Y‘a451n9 —-> v2;— M11146“ 51’ MMWﬁlr )wwzés 1’ 11151172 4% m? 219-1132 f 1 01:45.11 eseaﬁ f5: .4: £— 1” 1.11 6 5’ 6 {f 11 3“ .1 1} 1/ X J .1. 4 * ‘“ ” C321,“ waméew‘ “mgmmﬁm mwfmjfﬂ ...
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Key_Quizzes - #1 Name Solve the foliowing problems Show the...

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