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 . 12. The cap of the sphere x 2 + y 2 + z 2 = 16 , for 2 2 ≤ 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 . 12. The cap of the sphere x 2 + y 2 + z 2 = 16 , for 2 2 ≤ z ≤ 4
Solution Summary: The author explains the parametric description of the sphere's spherical coordinates.
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.
12. The cap of the sphere
x
2
+
y
2
+
z
2
=
16
,
for
2
2
≤
z
≤
4
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.
Sketch and identify the surface given by x? + 4y + 42² = 0.
Describe the surface with the parametric representation shown below.
r(u, v) = (v cos u,v sin u,5v), for 0 ≤u≤2, 0≤v≤2
Select the correct choice below and fill in the answer boxes within your choice.
OA. The surface is a sphere with its center at
OB. The surface is a cone with height of
OC. The surface is a cylinder with a height of
..) and a radius of
and radius of at the widest point.
and a radius of
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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