review quiz 1

# review quiz 1 - Review Quiz#1(20 points Math 200 Name K423...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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’ ...
View Full Document

## This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

### Page1 / 4

review quiz 1 - Review Quiz#1(20 points Math 200 Name K423...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online