Parametric Name ______
1. Suppose that the equations of motion for a paper airplane during its firs 10 seconds of flight are .
At what time was the airplane flying horizontally?
At what time was the airplane flying vertically?
What are the highest and lowest points in the trajectory, and when is the airplane at those
points.
Find and evaluate at the indicated point or parameter.
Find all points of horizontal and vertical tangency to the curve.
4. x = t2 – t + 2 5. x = 4 + cos
y = t3 – 3t y = -1 + sin
6. Find the distance traveled by the particle along the curve . Set up only.
7. A curve in the plane is defined parametrically by the equations x = t+ t and y = t+ 2t. An equation of the line tangent to the curve at t = 1 is ??
(a) y = 2x (b) y = 8x (c) y = 2x - 1 (d) y = 4x - 5 (e) y = 8x + 13
8. The asymptotes of the graph of the parametric equations x = , y = are:
(a) x = 0, y = 0 (b) x = 0 only (c) x = -1, y = 0 d) x = -1 only (e) x = 0, y = 1
9. Which of the following integrals gives the length of the graph of y = tan x between
x = a and x = b, where 0 a b ?
(a) dx (b) dx (c) dx
(d) (e) dx
10. Let f(x) be a solution of the differential equation y´ + y = eand let f(0) = 2. Then f(1) = ?
(a) 1 (b) (c) (d) (e) 3
11. A particle moves on the curve y = ln x so that the x-component has velocity x´(t) = t + 1 for
t ≥ 0. At time t = 0, the particle is at the point (1, 0). At time t = 1, the particle is at the point
(a) (2, ln 2) (b) , 2) (c) , (d) ( 3, ln 3) (e) ,
12. If x = t- 1 and y = 2e, then =