(a) Find parametric equations for the surface of revolution that is generated by revolving the curve z = f x in the x z -plane about the z -axis . (b) Use the result obtained in part (a) to find parametric equations for the surface of revolution that is generated by revolving the curve z = 1 / x 2 in the x z -plane about the z -axis . (c) Use a graphing utility to check your work by graphing the parametric surface.
(a) Find parametric equations for the surface of revolution that is generated by revolving the curve z = f x in the x z -plane about the z -axis . (b) Use the result obtained in part (a) to find parametric equations for the surface of revolution that is generated by revolving the curve z = 1 / x 2 in the x z -plane about the z -axis . (c) Use a graphing utility to check your work by graphing the parametric surface.
(a) Find parametric equations for the surface of revolution that is generated by revolving the curve
z
=
f
x
in the
x
z
-plane
about the
z
-axis
.
(b) Use the result obtained in part (a) to find parametric equations for the surface of revolution that is generated by revolving the curve
z
=
1
/
x
2
in the
x
z
-plane
about the
z
-axis
.
(c) Use a graphing utility to check your work by graphing the parametric surface.
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter
x-2, y-t
++
-1
0.5
05
05-
-05-
0.5
+
--05
A wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 790 cm long,
and 250 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale).
P
790 cm
250 cm
Write parametric equations for the position of the point P as a function of t, time in seconds after the ball
starts rolling up the ramp. Both x and y are measured in centimeters.
I =
y =
You will have a radical expression for part of the horizontal component. It's best to use the exact radical
expression even though the answer that WAMAP shows will have a decimal approximation.
Find parametric equations for the curve, and check your work by generating the curve with a graphing utility
The portion of the circle x2 + y2 = 1 that lies in the third quadrant, is oriented counterclockwise.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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