review quiz 1 - Review Quiz #1 (20 points) Math 200 Name:...

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Unformatted text preview: Review Quiz #1 (20 points) Math 200 Name: K423; 02/24/10 Group: 1. Find the unit tangent vector T(t) to r(t) = 4% i+t2 j+ t k at the point with parameter value If =1. ?‘(1’):<2t%‘12t)t> firm: Fix) a (22» -—+--— wail» FIC‘) : '< 2) a) l 5 i ‘12" lz‘H 3) 2. Find an equation for the plane that contains the two parallel lines given below: x=2t+1 x=2t nth-cult” uec‘i‘or “For [Hie K5 = (21-!) I) y=—t+3 y=—t—2 __’ z=tvl z=r+1 vechr fuzfigmme V = <0‘l1”3*3)l“(~i)> i=0 =3 fut (Jig—i) got-J” (0,4,!) A A : 4-1) ~s) 2 > ‘ ‘ A H ‘6“ La“ A normal oed‘or ,__, __ ___.‘ x... t: L J 1:; blunt-t 0-?- pl-’ 42. 46v H-Q. Flame n - I" U “1 2 Y‘ ‘(x1713>"nl<113f0 ’ 3x—53—Hiz 3—is+u:-l '4 <3l‘s)”“> 3x-—S7~H2=—l 3. Give the name of the quadric surface below and give a sketch showing its orientation in 3-space. Label three points on the graph with their ordered triple. name: Ciiiph‘c QC:me Joli y=x2 +422 4. Sketch the space curve with vector equation r(t) = <1,2sint,2cost> . Describe this curve in words and indicate with an arrow the direction in which I increases. 2 Pt circle of Main}: 2 cal-er 0,90) 2 {in 'Hne X3! {Alanna ‘ 5. Find parametric equations for the tangent line to the curve x=12 +3, y=14_1, ers atthe point (2, 0,1). g ‘ 1‘ 3. O l : N-ll " (“l2 4- 1:) til-11 t3) P { J ,) correspond: 1L; 1; 1 “Flu = {DH-I, Hi 3+3 Ued-or QIDUQJ-t‘on b‘F "H39. l'Qhfia-cl- invite 41' t3"! : LN : Ft!) +73%?!) = {210,0 +t<3)'+,3> Pamme‘l-rgg €5UQ+tonS are - x: y : Lit) '2: 6. Find a vector equation for the curve of intersection of the circular cylinder x2 + y2 = 4 and the parabolic cylinder 2 = x2 . L.th X:t lot He {wrangler ~‘ Lil‘- X =Qcost i I 1:), Or; 7: 2 $\-l'\t ya: Lf‘xzz W‘ttéytimi 2:)(1: (R‘O'rg H l?» e4 ‘POr +ke Curve “(fl :5 (t) V‘i‘th, ft) {ngflfcl‘l‘w me = (kl—W)?» The r (acastpsittaw‘w - Mth 05,5011- 7. Convert the point 1 2 ,%,5] from cylindrical to spherical coordinates. f: ‘02 / 2"; a : vhf l (‘1: xiii-7L -— 3‘ L (05¢? : 3%: TI—ai J01: XL+7L*9L:$+GC) : ‘chos" 1': 2n; 3 2‘ m, +kspmrsal Comma, m (rm) 17/3) 8. Find the arc length parametrization for the line r(t) = <1—r,2t,3 — 2t) 1; rm : (“;12”1> ; llrt(+)ll=lll+‘t+'f =3 I t d It) :j ._ t 0 llrlmllld“ " j3clu 3 3~Ll = '37: 0 O The HitlftSe 0'? {Sgt “in t: gin Till”, 'HW- Gun; Pomme+ft.2~a1£tton OF ‘er L; -—3 \z w =F(%> = we) 24% 9. For the space curve r(r)=<2t,rz,%t3>, 03:51, (a) Finditslength. {that} t1) MFR)“ : dw+wt1+tq 3 W rl'Lt) = < 012131;) = JV“- I 1 =[Q—‘Lfldt -: t *J‘t] - ‘L +23 '2‘ 0 Km : H FEU xF‘HER 3 .‘\ ’3 I; “J! .4‘ u“ t. “MW mer :\ 1’2. l \ = H <2,“'f1‘+>l\ o 2 2 3 1 -_- ( 1’ “41*? _ Hg : :1 Wu)” : mpg ” '2') q I 12.9.»): 10. Parametrize the osculating circle to the curve y = lnx at x =,€{. 4 ‘— 4 " : "J :5 P(x)=(x,9nx> l "(x)\ 7“ x > 7 x“ ___,. l “'(X) - [‘fi‘yclxr)?‘ L r(x):(l)x> -1. - — ""L2. _ x K _ ‘ a : J—r— ‘- — 3 .- 1 A y]. (}*’)}<‘1)X (\"")l:?")/l 2 (HI) 3 "Farm:qu icky» . =23: USQ (")IEJH‘> 4;“. d';ec+:ov\ of K3. l-Jlg J. J_ _| NH): X)“> -— x,"> {X 4) -v -L m — 2' -——~L-. MU): r 4W7 h4éfi>ll 03511 I) kw“ ’ l “.4 .4 3’ Utah‘- o‘F OSCBKCJ'ENJ Cx‘mle. 097 = r03 + W!) U“) : (’,°>+22"|Il:i (if!) 1v; 'er Pammei'n‘hfifon 0+ ‘er OSCU led-1&3 Gui-dais : < g; ’1) C“) = < 3/10 +2Z<cost, an), ost <21:- 11. Suppose a particle traveling on the curve r(t) has acceleration vector 3(1): costk (in units of m/sz), initial velocity v(0) = i— j , and initial positionr(0) = i . (a) Find a vector equation for r(t). "3%) t N + Ufa) O = (0,0, mt) + (1,4,0 : <1/*|)J‘I}\tj _ t ‘l [GUJJLL :J(O/O/COSK>JLL ‘-'-' (OIOJSI-Iw.) A -t 1‘ Mt): qulau = f(l,-I)s.ha.>ala O 0 t _s +r-(o) : (1-) -t/—mrt+n>+(1,a(a> 0 (b) Find the speed ofthe particle at t=7r/2 s. I < t—I- l ) -‘t, - (est +l) : (k)‘-UL)-'(OSLL>J UM?) =II‘J(%)H =ll<1,~u\>ll = \Fs MA). 12. Let r(t)=<e’,l—t>. Decomposition a(t) into tangential and normal components at t: 0. -.b ’ .__. Wt): r(+)= {etJ-1> J u(ol= (1,4) .3 _ I .4 S [1 m ghdaJ' “J _JL(£-__<_IJ:L>«: HP (0 “+3 To 1 ' T(°)'UU(OJH Vi ( 1 _. -.. _ _:f" .".' : (llo)'<J-}) '— i Sivplf («truffle 0th? and N (lg-13 =55, “Ci-1‘? Ct» : "J - — —- LC ~ “aawne was” — as: 75(0): i a _.J_.<.t¢3_ £51) _ '9 "" " i 1 "' :2 2 H1931 Ulri'i'c‘ilw derNPOSJPCOh'. "( k )2 < ’ "‘-= defies-“Ki 2 §?+‘% N where ¥=<‘§,-% an: .._I "4 IE:- Ll‘ewqfoh <uo> = '%<% -§>+~l§<’-§,"§-’:> N = < a) 1’ ...
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review quiz 1 - Review Quiz #1 (20 points) Math 200 Name:...

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