worsheet 8 - Math 200, Spring 2010 Worksheet 8 Section 13-4...

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Unformatted text preview: Math 200, Spring 2010 Worksheet 8 Section 13-4 Curvature 1. Compute the curvature of a circle of radius R. A55Ume aft-ale 055 deu: R19 cent-Erato of "sad" at; "Fifi = < R 035 ‘1'.) R such) 7%“ ‘- (-Rsrnt, Rcosi'7 , n?’(+)ll = R IT cc... be. pammefrtz-ea 0 d 2' m I. " St-ht R St) -— ~ "A .1! o “1:05 "7.le < R a w a. r_ < S\ t , cast? ‘ “Ta” ‘ I T (if) = <- Cost) ‘- snkt> , “Tm” = Heme’ Kw‘ )\?'{+3\l__§ 2. Calculate the curvature 1((1‘) ofthe twisted cubic r(t)=<t,r2,13> . m) : <t,t‘,t‘> =3 leflltfliifl Wivali“ 1.x {x n y=K(r) ..Il __"I \ if: mum)"— \\ 31: fl = “til—egg) b '2 6t ._:' .40 I , _ Mr (1-) x r (HM ‘2 LUZ) - --———-::—(—-———-—-§—v FIGURE 6 Graph ofthe curvature 1((1') ofthe twisted cubic rm: (t,t2.t3? \\ r (til) : 364;" + 35th H '( X+WtL~QtU 3/2 Maximum curvature at r = 0 FIGURE 7 Graph of twisted cubic rm 2 (LI-3,13) colored by curvature. 3. Compute the curvature of f (x) = x3 —3x2 +4 y at x = 0,1, 2 . H») = x13)?” => Wu: 3x‘-tx 3th =éa~s - Wm: 1c -4 mo - —————————- : v—i—i—fit ,. (\+¥’rx)‘)% (HM-m); iéxvéi for) 2 x3 — 3x2 + 4 Curvature FIGURE 8 Graph of ftx) = x3 —— 3x2 + 4 and the curvature fix). a (I, 019) Corr-e spends +9 “[7 : o 4. Find the vectors T, N, and B at the point (1,0, 0) on the curve r(t) = <cosZr, sin 2t, 2t) "em- 1MB 1 <-Qs{“2t,1cosat 2) "F?+)=<—3srn2t,1cosat,2> " A! "W11 an mm = m = no: 2 “Sink cant i ._. J, __,J < tr)- J U3. J 13> 1 <0) G 5. Find aparametrization of the osculating circle to y=x2 at x=1. __ Let {:(x): X1. use +1“; gave. me‘h‘i firqit‘dn. : <x)xa> .4! .s 1"{X : 1 ) Stern: Fina e and m. ) <52" F. ¥x:1 K(¥)=_M.L : k1”: % {£62, :éx (1+ ¥'(x)1)J/I (1*thz) 3" ) '5 A“ 9‘“; we; +0 301: 9’00 =1 : - (1 1x) --—’z 2 _. fl - ‘ - l * _.J._~_. : _ < 2.x 1) dired‘on fl m on 69 ( l-Htxa') y; > T06 _‘ “' mrl‘e Hm? :I; (Rx ,1) 1', . ( 1+ ‘i-x‘) V1 ,3 .ikis derive-live/ orfioaond +5 F- . . . W19" {biz} refile a. 5.1“ of 4,139qu $0 (flax)! ) fmu;¢j?5 5171:? H59";- dof‘ Mud- “ k". ""’ —- We Q'sch ‘cm o-f' K], > we): 33L; = 4—2,. s __, we i\<“l)¢)\)n W ) 2: . Fin-“d H9 (Ruhr a; +k3 csculq‘i‘fi‘a CIY-ficle' 09 = m) + m" Rim = <m> + %‘-<-e,i—s>= = <I,x>+%<~2,t> = (4,19 Sire? 3.“ Parame+v?l~e 'er OSCUia‘i'Iis cx'rele J 5%. : L: R km ‘3 ) (adapt-1);.) y “em = 69,3) + 1231mm“) J Homework #8 Reread Section 13.4 (Due 2/19) Do Section 13.4 Exercises: 1, 3, 7, 9, 13, 14, 18, 19,23, 35, 36, 43, 49, 53 Prepare for next class session: Read Section 13.5 ...
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worsheet 8 - Math 200, Spring 2010 Worksheet 8 Section 13-4...

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