{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

worksheet 6

# worksheet 6 - M Math 200 Spring 2010 Worksheet 6 Name K2...

This preview shows pages 1–2. Sign up to view the full content.

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: M Math 200, Spring 2010 Worksheet 6 Name: K2; Section 13-2 Calculus of Vector-Valued Functions 1. Evaluate the following limits. a limsin2ri+costj+tan4tk b. 1h???” t J+4tk —>Il' 1—) + A ' ¢_-. . t-l on =‘Q‘m Sm'lti, +JKC05'EJ +k‘i‘anﬁk : “ii-'22; eff-1+0 {911' ‘t'UlT {rm 9 . bag a A = 6‘: ‘3 +OK : "d two J ‘ J 2. Find the derivative of the vector—value function r(t)=sin_lti+\ll—t2 j+k. "A 9 nl .- I I Fl rm: <5.“ 1,0134?) 1» => m) = f; «Mfr-v“, n <ﬁ‘f-s , é<l-t‘)"‘1—2*).°> 'L 1. ’L 6‘) 3. If u(t)=(sint,cost,t) and v(t)= (t, cost, sint) ,ﬁnd ——[u(t) )).v(;] :<W:c J 0"‘7 J W") '39], '- I (H u111+ 32+) 111+) '-‘ (Sid: (os’t 4%) {1 asin‘l'. 405’s) «r (out -Sm't D (t, (05‘! Salt) '- Smt "COTE. Sin'}. +t‘cost + tcoS'l.‘ — Sm‘l: (0H. 1- Sud: 1' 2t Cost 4' 25nd: ‘ 511121: 4. Suppose rl(t)=(tz,t3,4t), and r2(t)=(t‘1,1+t,2). a. Let F (I) = r] (t) 0 r2 (1) Calculate F '(t) ﬁrst using the product rule, then secondly expanding the dot product rI (I) 0 r2 (1‘) and differentiating. _. ,4 3 Flt] = nod-131+) =30: 4;: st>- {t 1+1. :1) = £+t1+1ﬂ+8t =ti+t+ﬁt Fm- - 'Fm. p [+)+?‘(+)- 131+) rte: +3, L1-4:) {- -t:1,o>+(2t,3+j H) (til-H: 2) _. = ~1+r7 “2+2; «12¢ +3 =94: +2 Hf“ ‘3 o.— F'K’r) = ﬁche)- Tum]: {EH +t3+q.t1- * .tji'tﬁi b. Let G(r)= r1 (1‘)er (t). Calculate G' (t) ﬁrst using the product rule, then secondly expanding the cross product rI (t)xr2(t) and differentiating. A (SH) "-'- rt (3..) An\$tiu ' —- —- ¢ ._. —- O K L . K 3‘ “ ‘ 5 U") = NH) 3 mm min mm = i‘ t3 “A * in: i1 '1 = (96‘— Bt-ﬂu-Wﬁt‘k t“ i *3 {"Ht 2 as q H or get): tttth'tvx A _ .L 3 h (J J <‘t,l+t’1>- 1" 1:.5 “P17 ' (2t1%"‘ft)c‘ [if ‘9) +9”; 1.‘ 1+1. 2 5. Evaluate %r(g(t)) usingthe chain rule. :3 5ft) " (‘tt 3*- 9) c. "AH-‘3 ~+§t l: a. r(t)=<t2,2t,4>,g(t)=e' b.r(t)= (23in2r 6cos2t), g(t)=t2 .4: t t .- TL ) 'W - 1t rm: (11:20) 3(hl'4e NH (446511: “115‘“ ‘3 _.[ t i 731+»: Flaung (’0 1- Fe) 1+ t) ~ {1 1 d It: ‘3 H) *{3 ”3‘ :1 f9 ._. (Ly-(05211:. —n\$ml’° >1“ 6. (a) Sketch the plane curve with the vector equation r (t) = e‘i + e_‘j . 7 1=e"°=“’z=-L s ' ttk in -1 (b) F' d ’(t) e x ) 0 can: as eat-- 0 “hr 0‘!- 1'”: in r . .. __ 3‘ -t __ t.“ _ “+3-etwe 5:311”) - e are? (c) Sketch the position vectorr(t) and the tangent vector r’(t) . _ ._’ 1" I) atthepomtwhent—O. 1'10) : L. *3 A "9(0): in new" it 7. Find the unit tangent vectorT(t) at the point when t=1 for the vector function r(r) = 4J2 i+t2j+tk. .4! -I .2. ? 'I r (t) * “'1 (Fit) +13 H "J '4‘ 1‘ 1‘ '5‘ K “ a “ - '1 '1‘ 2 '3- .1." T10 = .1119. 2%— : -§(23-23*—K3 ~ 3'1. raw-31: tit-Tn“ m 8. Find a parametrization of the tangent line at the point indicated. a. r(t)=(cosZt,sin3r,sin4r), t=-E b. r(t)=<t2,t4), t=1 11.1% 3 (-19:32k, Stu 5t ‘t-te: '1-1:> "53119 :- (2'1: ‘tt‘? 4 .1 .1. J -‘ 4 I ..I.I H151: rant-trﬁﬁ L”) = NIH-“trim = ((051; sin 15,SAR)+1:<~15;,J‘I 3m”; 41,” +t<3ﬁ|> 3 (1+1t,1+'t-t> " _¢+t> ’ .“H-can) 2 , " {‘31: .3. " anti . . . - r I t 9. F 1nd parametric equlmons fo’1’ étangent line to the curve With pararnetnc equations x = e , y = te , z = te at the point (1,0,0). (1,0,0) con-upon“ +3 '1.‘ 1 0 - 05% :(f) -: "ti-(ta) + 't :Y‘t.) _‘ __, t 'L a, t. I ﬁt) “(e Itetjtet> :3 Mt) 1' «Start-e“, ltlett-et > A A l m: +20; H-t) = H0) *- £11761: (11°,°>* ’c< 1,1,1) = {1+t,t,‘t> ‘9 urmmztrCo QEM-‘hm" are X: 1+t ’73-'12, i=1; 10. Evaluate the integral (2!,4t,-—cost>dt U72 (unponon‘t‘ ”3w {Wham-+11% .. ‘ ‘ \ 1°03 H-tJ—(ost7d‘t. = <{21at,);'~+tat, )_costat> :<{*‘ at‘\‘ - shah 3 6 0 l o J 11. Evaluatetheintegral I(cos7rti+sin7rtj+tk)dt. 1' <1 ) '1 ) - 5112(1)» 5(c,,,,t{, sinnt§+tE)d+‘=11<osﬂfdt—)i +15-st'n1rtat)‘; +(Stat)k ‘ p—h - é Sakn’t E -11; (”“3 *it‘f-‘t + c 12- Find rtt)ifr'(r)=ri+etj+terk and r(0)=i+j+k. —-I .. .31 A A a ‘ ' -. t. + “H'STH‘M=11tteetj+tett<)dt it +e ,-+[’Ce MK C .—I -,:(,,,3_§+E' = f+§+|< =3 c= “'2“ if I p Homework #6 Rercad Section 13.2 (Due 2/08) Do Section 13.2 Exercises: 1, 5,11,13, 17, 18,19, 20, 21, 27, 33, 35, 41, 45, 47, 51,55, 62 Prepare for next class session: Read Section 13.3 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

worksheet 6 - M Math 200 Spring 2010 Worksheet 6 Name K2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online