1. The problem statement, all variables and given/known data A particle moves in the xy-plane so that at any time t ³ 0 its position (x,y) is given by x = e^t + e^-t and y = e^t - e^-t . (a) Find the velocity vector for any t ³ 0. I know how to do part a it is simply (derivative of x, derivative of y) (b) Find lim (dy/dt)/(dx/dt) (t approaching infinity) What does this (dy/dt)/(dx/dt) tell us? I know dy/dt is going to be y component of the velocity and dx/dt is the x component of the velocity. Yet, simply dividing y component of the velocity at certain t by x component of the velocity at certain t ... what does this mean? So, i just attempted to find the limit of (dy/dt)/(dx/dt) as t approaches infinity without actual understanding. (e^t - e^-t) /(e^t + e^-t) ;the first one, the derivative of y, the second, the derivative of x In this i run into the problem of the function being undefined. I fiddled with it a little but could not find a way to avoid the problem .... Help me deal with my stupidity, (c) The particle moves on a hyperbola. Find an equation for this hyperbola in terms of x and y. i do not know how to isolate t in either function x or function y (in order to subsitute that for t in the other function ) (d) On the axes provided, sketch the path of the particle showing the velocity vector 2. Relevant equations 3. The attempt at a solution I need your help. Thanks.