1. The problem statement, all variables and given/known data AN object moving along a curve in the xy-plane is at position (x(t),y(t)) at time t, where dx/dt=Arcsin(1-2*e^(-t)) and dy/dt= 4t/(1+t^3) for t>or= 0. At time t=2, the object is at the point (6,-3). a. 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 approaches infinity. b. The graph of the the curve has a horizontal asymptote y=c. Write an expression involving an improper integral that represents this value c 2. Relevant equations None 3. The attempt at a solution a. So I got m(t)= 4t/ (1+t^3)*Arcsin(1-2*e^(-t)). Then will my limit be 0 ? b. Will the expression be: c= integral ( (dy/dt) / (dx/dt)) from 0 to infinity ??