Name:
WA 3, p. 1
Name:
University ID:
Thomas Edison State University
Calculus II (MAT-232)
Section no.:
Semester and year:
Written Assignment 3
Answer all assigned exercises, and show all work. Each exercise is worth 5 points.
Section 9.1
2. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve.
{12cos
22sin
xt
yt
=+
=-+
8. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve.
{2
2
1
1
xt
yt
=-
=+
12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve.
{2
t
t
xe
ye
-
=
=
22. Find parametric equations describing the given curve.
The line segment from (3, 1) to (1, 3)
28. Find parametric equations describing the given curve.
The circle of radius 5 centered at (–1, 3), counterclockwise
Section 9.2
6. Find the slopes of the tangent lines to the given curves at the indicated points.
{2
1
sin
xt
yt
=+
=
(a) t = –π (b) t = π (c) (0, 0)
8. Sketch the graph and find the slope of the curve at the given point.
{3
42
54
xtt
ytt
=-
=-+
at (0, 0)
20. Given the parametric equations for the position of an object, find the object’s velocity and speed at the given times and describe its motion.
{3cossin3
3sincos3
xtt
ytt
=+
=+
(a) t = 0 (b) 2
t
p
=
26. Find the area enclosed by the given curve.
{sin
cos
xtt
ytt
=
=
, 22
t
pp
-££
28. Find the area enclosed by the given curve.
{3
4
4
1
xtt
yt
=-
=-
, 22
t
-££
Section 9.3
4. Find the arc length of each curve; compute one exactly and approximate the other numerically.
(a) {cos
sin
xtt
ytt
=
=
, 11
t
-££
(b) {2
2
cos
sin
xtt
ytt
=
=
, 11
t
-££
8. Find the arc length of each curve; compute one exactly and approximate the other numerically.
(a) {2
4
4
xt
yt
=
=+
, 12
t
££
(b) {3
362
3
xt
ytt
=+
=+
, 12
t
££
12. (a) Show that the curve starts at the origin at t = 0 and reaches the point (Ï€, 2) at t = 1. (b) Use the time formula (3.2) to determine how long it would take a skier to take the given path. (c) Find the slope at the origin and the arc length for the curve.
{0.6sin
20.4sin
xtt
ytt
pp
p
=-
=+
16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.
{2
4
4
xt
yt
=
=+
, 12
t
££
(a) about the x-axis (b) about x = 4
Section 9.4
2. Plot the given polar points (r, θ) and find their rectangular representation.
(2,)
p
8. Find all polar coordinate representations of the given rectangular point.
(–1, 1)
12. Find all polar coordinate representations of the given rectangular point.
(2,5)
--
14. Find rectangular coordinates for the given polar point.
3
(1,)
p
-
22. Sketch and describe the graph of the polar equation and find a co
esponding x-y equation.
3/4
qp
=
26. Sketch and describe the graph of the polar equation and find a co
esponding x-y equation.
2sin
q
=