m251ex3key - A~ MATH 251 I<~ Section 504 Test III April 7...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
A~ I<~ MATH 251 Section 504 Test III April 7, 2004 Name There are a total of 5 problems. 1. Given the circular helix x(t) = acos2t } y(t) = asin2t z(t) = bt 0 .s t .s 311"; a, b > 0, (i) Let s(t) be the arclength variable of the circular helix: 1. 2. 3. 4. 5.- Total s = s(t) = It ds. Determine s(t) as a functionof t. (7.5%) ...... (ii) Determine the unit tangent vector T(t) on the curve at time t. (7.5%) (Hi) Evaluate the line integral J y sin z ds, where b = 2 while a > 0 is arbitrary, by C using the s variable. (iv) Repeat part (iii) above, but by using the t variable. ( i) (+ .4 Stt)= Jt> h'(~lt:{z ~, ( Y (i):: -Zo.. ~7.,t) 2..a.~1..t ) h) l -a. I ( 1. -a.- a. J Yl... ?(-c) = (-LA ~2...t) +-C2..0.. ~:z..t) +- b ::: (iftt2.(~l,-t+-~t,t) +-b3-J y~ (4tt2-+b1.J Yz. ~tt:);:. ); (447..+ bt.y\:(z;;~ ~o.."1.+hi. + 1 "-~i I 7t~<.I :::- (7.5%) (7.5%) -
Image of page 1

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

View Full Document Right Arrow Icon
.. ~ Y 'ct) --. - I (II) T Lt):. ivJ'(t)/ - ,J~~ ~~(.../:) ) 2A un (2.t) , h ). U'9 ) 't~r.(L: ~ 0..4.W..~t) ~~t)d..S ~ C. j 31\J fc'. \-~1,.. = ~ 2 . 2. )d. a.~ -> ~ --5)- f) t4~"+i," ) ( f. L - I H.e.--, ~ t:::. t - S) ~ wL- t= 31'() S:: J4~1. -l-b'l.. 37f" ~ ~~~.. ) .:: J 4a>-t 2&. . 3if ) '.4 "",'T4 . 2. S d.~ .4-tM.- :: ~ ~ (4 J..+{ () """"t"' 2 5 ) 61t4 Q t\ ( -L ( i-CAn..- ,: =.(k 2. ..J ~ ~I '" ~ ()..s I S:6JfJ~ .,~ I 'lf.{;;i;i . ots ::. ~ '4~ .,..1 . 2.5 -.., 2. - -,4.:-- s:o 2 ~~~I S:. «' ::. 31\0- ~ 0. 2-./-1 . 01 S . (. r" ~ (1)') ) 1A-}.ls = ) ~ "":":z.r.~2.-t .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the 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