Parametric descriptions Give a parametric description of the form r ( u , v ) = 〈 x ( u , v ) , y ( u , v ) , z ( u , v ) 〉 for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane . 14. The cone z 2 = 4 ( x 2 + y 2 ), for 0 ≤ z ≤ 4
Parametric descriptions Give a parametric description of the form r ( u , v ) = 〈 x ( u , v ) , y ( u , v ) , z ( u , v ) 〉 for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane . 14. The cone z 2 = 4 ( x 2 + y 2 ), for 0 ≤ z ≤ 4
Solution Summary: The author explains the parametric description of a cone using the parameters u, v, and z.
Parametric descriptionsGive a parametric description of the form
r
(
u
,
v
)
=
〈
x
(
u
,
v
)
,
y
(
u
,
v
)
,
z
(
u
,
v
)
〉
for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane.
Describe and sketch the surface in double-struck R3 represented by the equation
y = 2x.
The equation represents the set of all points in double-struck R3 whose y-coordinate is ( insert answer) times their x-coordinate, that is,
{(x, 2x, z) | x is in double-struck R, z is in double-struck R}.
This is a vertical plane that intersects the xy-plane in the line
y = , z = .The portion of this plane that lies in the first octant is sketched in the figure.
(2) The figure below shows the contour diagram of g(x, y).
a) Mark the points on the contours where
b) Mark the points on the contours where
Iz = 0.
Iy = 0.
2
2
1
1
-1
-1
-2
-2 -1 0
-2
-2
-1 0
1 2
1 2
Thomas' Calculus: Early Transcendentals (14th Edition)
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