MAC 3473 Honors Calculus 2
Keesling
Review Test #4
Test Date
4/22/08
1.
Consider a circle of radius
R
rolling along the
x
–axis with the speed of the center
of the circle being
R
.
Give a parametric representation of the motion of the point.
Suppose that the point starts its motion at the origin,
(0,0)
.
The curve is called a
cycloid
.
2.
Determine the velocity and speed of the parameterized curve in the previous
problem.
3.
What is the arclength of the cycloid over one cycle of the curve?
4.
What is the area under the curve of the cycloid over one cycle of the curve?
5.
Consider the parameterized curve given by
x
(
t
)
=
t
sin
t
and
y
(
t
)
=
t
2
+
t
.
Determine the slope of the tangent line at each point on this curve.
6.
Find the equation of the tangent line to the curve at the given point.
The
parameterization is given by
x
(
t
)
=
1
+
ln
t
,
y
(
t
)
=
t
2
+
2
and the point on the
curve is
(1, 3)
.
7.
Determine the area of the region enclosed by the curve,
x
(
t
)
=
a
cos
3
t
,
y
(
t
)
=
a
sin
3
t
.
This curve is called an
astroid
.
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 Spring '08
 BLOCK
 Calculus, Conic section, parameterized curve

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