HELPPPPPPPP

  • chutieuthichbeer

    May 31st 2011, 3:01 pm
  • PROBLEMS

    1. Sketch and also describe the curve given by

    a) R(t)=(t,0,t^3) [-1,3]---> -1<_ t <_ 3

    b) R(t)=[8cos(t)sin(2t), 8sin(t)sin(2t), 8cos(2t)]


    2. Find a vector function that defines the curve of intersection of the cylinder x^2 + y^2 = 1 and the plane y+z=2


    4. Show that for any differentiable vector function R(t) of constant length the vector dR/dt is perpendicular to R at any point t


    5. Find the length of the following curves. Graph the curves.

    a) r(t)=[t^2, sin(t) - tcos(t), cos(t) + tsin(t)] [0, Pi]----> 0<_ t <_ Pi

    b) r(t)=[cos(t), sin(3t), sin(t)] (nagetive infinity < t < positive infinity)


    6. Determine the vectors T, N, and B and also the curvature k at any point for the following curves
    a) r(t)=[sin(t), cos(t), sin(t)

    b) r(t)= [t^2, (t^3)2/3, t]


    7. For the curve y=lnx find the point where its curvature is a maximum. What happens to the curvature as x---> positive infinity ?


    8. Find a point on the curve r(t)=(t^3, 3t, t^4) where the normal plane is parallel to the plane 6x + 6y - 8z = 1.


    9. Find the velocity and speed, and the tangential and normal components of the acceleration if the position of an object is given by
    a) r(t)= i + (t^3 - 2)j + 2tk

    b) r(t)=[1; (1+t)/t; (1-t)^2/t]


    10. Find T, N, B, the curvature and the torsion for the curve .
    r(t)= [1sin(t)/square root 2; cos(t); 1sin(t)/square root 2]


    11. The force F(t)=(t^2, t-1, 1) Newton is applied to an object of mass 2 kg. At time t=0 the object is at the origin and has a velocity v=(1, -1, 3) . Find its position at time t.

  • mltr

    May 31st 2011, 3:32 pm
  • 1/ Hum có gì khó ... let t=-1,0,1,2,3 ... the other problem t =pi/4, pi/2 ... so on .. connect the dots ... if not sure how the curve go, check value of mid-point (b/w dots)

    2/ Find R(t)

    4/ dR/dt is a tangen at t ... R(t) x dR/dt = -1 (check formula again .. lâu rùi hủm nhớ rõ lém)

    5/ Find length = use line integral

    6/ hum nhớ

    7/ at x=1 .. after that, you can see on the graph .. google for lnx graph

    Will look at other problems later


Designed by squallions © 2004 - 2009 maiyeuem.net (MYE). All Rights Reserved.
All posts and comments are owned by the poster. MYE is not responsible or liable for any content its member posted.
Mọi chi tiết, xin liên hệ: contact
Powered by phpBB © 2001, 2002 phpBB Group