{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4.2 pt 2 (1) - 240 4 Vector-Valued Functions 3(sin 3t cos...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 240 4. Vector-Valued Functions 3.. (sin 3t, cos 3t,2t3f2)-,0 g t g 1 4.(i+1,[email protected]+7,§t2);1gig 2; 5. (anti). 1 s t 52-, 6. (t,tsint,tcost);0 g t 5 11' defined by c(t) = {2 cost,2sint.t.. ,if2a' 3: g 4n. t): (1,3t2,t3),if0§tg 1 a 7. Find the length of the path eft), D g t 5 2a and C(t) == (2,t — 211,16) 8. Find the length of the path C(t), where cf C(t) = team], if 1 g t g 2. _ ath C(t), defined by s(t- s the distance a particle traversing the trajectory- 5 out at time a; that is, it gives -' d the arc length functions for - = (cos t, sint,t), with a : f}. I; UleNldT. mpresent c will have traveled by time t if it start length of c between C(91) and C(t). Fin curves aft] = [cosht, sinht,t) and fit) 10. Let c be the path C(t) = (2t,t2, logt), defined for t > 0. Find the length of c between the points (2, 1,0} and [4,4, log2). 11. Find the arc length of the path C(t) : (t,tsint,tcos t) between (0.0. and (17,0, —1r]. 12. Let C(t) be a given path, a S t g b. Lets = aft) be a new variable, whe is a strictly increasing C:l function given on [cu b]. For each s in [0501), of there is a unique is with Mt) = 3. Define the function (1 : [15):(tt)I cc[b)1 —~ by d(s] = C(t). The path (1 is said to be a reparametfization of c. (a) Argue that the image curves of c and d are the same. that c and d have the same arc length. (b) Show (c) Let s = aft} = I: Hc’[r)lldr. Define d as above by d[s) : C(t). Sh that d ‘ d is called the arc length reparametfization of c. —» R3 be a smooth path. Assume c"(t) 75 0 for any t. 15. Let c : [ ,b] (1 since RTE)“ = 1- vector (2’ (t) / Hc’ (t) 11 = T(t) is tangent to c at C(t), and, is called the unit tangent to c. = 0. [Hint Differentiate TUE) -T(t) = 1.] (a) Show that T'(t} - T(t) for T’ (t). (b) Write down a formula in terms of c ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern