Results 1 to 1 of 1

Thread: Object along a curve

  1. #1
    May 2008

    Object along a curve

    I'm also having trouble with this problem. Any help would be appreciated.

    An object moving along a curve in the xy-plane is at position (x(t), y(t)) at time t, where

    \frac{dx}{dt} = sin^{-1}(1-2e^{-t}) and \frac{dy}{dt} = \frac{4t}{1+t^{3}} for
    t \geq 0. At time t = 2, the object is at the point (6,-3).
    (Note: sin ^ {-1}x = arcsin x)

    a) find the acceleration vector and the speed of the object at time t = 2

    b) the curve has a vertical tangent line at one point. At what time t is the object at this point?

    c) Let m(t) denote the slope of the line tangent to the curve at the point (x(t), y(t)). Write an expression for m(t) in terms of t and use it to evaluate lim m(t) as t -> infinity.

    d) The graph of the curve has a horizontal asymptote y =c. Write, but do not evaluate, an expression involving an improper integral that represents this value c.
    Last edited by akwingzero; May 31st 2008 at 10:26 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Apr 25th 2010, 08:23 AM
  2. If an object
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 12th 2009, 01:57 PM
  3. Rectangle intersection with curve(Object)
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Jun 5th 2009, 05:06 AM
  4. Parametric Curve and Travelling Object, help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jul 4th 2007, 02:46 AM
  5. An object...
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: Jul 20th 2006, 05:10 AM

Search Tags

/mathhelpforum @mathhelpforum