No Calculator Question: A particle moves in the xy-plane so that the position of the particle at any time t is given by:
x(t) = 2e^(3t) + e^(-7t) and y(t) = 3e^(3t) - e^(-2t)

a) Find dy/dx in terms of t and find
lim dy/dx
t-∞

b)Find each value t at which the line tangent to the path of the particle is horizontal or explain why none exists.

c) Find each value t at which the line tangent to the path of the path of the particle is vertical or why none exists.

Question

No Calculator Question: A particle moves in the xy-plane so that the position of the particle at any time t is given by:
x(t) = 2e^(3t) + e^(-7t) and y(t) = 3e^(3t) - e^(-2t)

a) Find dy/dx in terms of t and find
 lim     dy/dx
t->∞ 

b)Find each value t at which the line tangent to the path of the particle is horizontal or explain why none exists. 

c) Find each value t at which the line tangent to the path of the path of the particle is vertical or why none exists.