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
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 ??