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 . 15. The portion of the cylinder x 2 + y 2 = 9 in the first octant, for 0 ≤ z ≤ 3
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 . 15. The portion of the cylinder x 2 + y 2 = 9 in the first octant, for 0 ≤ z ≤ 3
Solution Summary: The author explains the parametric description of a cylinder x2+y 2=9 at the first octant.
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.
15. The portion of the cylinder x2 + y2 = 9 in the first octant, for 0 ≤ z ≤ 3
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
Give a parametric description of the form r(u,v) = (x(u,v),y(u, v),z(u, v)) for the following surface.
5√3
2
2
2
2
The cap of the sphere x + y + z = 25, for sz≤5
Select the correct choice below and fill in the answer boxes to complete your choice.
(Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2x. Type exact answers in terms of .)
O A. r(u, v) = (5 cos u sin v,5 sin u sin v,5 sin v) for
Sus and
SVS
O B. r(u,v)= (5 sin u cos v,5 sin u sin v,5 cos u) for
OC. r(u,v) = (25 cos u,25 sin u,v) for
O D. r(u,v)= (5 cos u,5 sin u,v) for
sus and
sus
SVS
sus and SVS
and
SVS
Find a parametric representation for the surface.
the part of the sphere
x2 + y2 + z2 = 16
that lies between the planes
z = 0
and
z = 2
3
.
(Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.)
where
0 ≤ u ≤ 2?,
?
6
≤ v ≤
?
2
University Calculus: Early Transcendentals (4th Edition)
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