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Deck 9: Vectors and the Geometry of Space
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Question
Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
If 
in cylindrical coordinates, find rectangular coordinates of Q.
in cylindrical coordinates, find rectangular coordinates of Q. Question
Convert 
from spherical coordinates to rectangular coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from spherical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Convert 
from rectangular coordinates to spherical coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from rectangular coordinates to spherical coordinates.A)
e. b. f. c. g. d. h. Question
Convert 
from cylindrical coordinates to rectangular coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from cylindrical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Convert 
from spherical coordinates to rectangular coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from spherical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Convert 
from rectangular coordinates to spherical coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from rectangular coordinates to spherical coordinates.A)
e. b. f. c. g. d. h. Question
Convert 
from rectangular coordinates to cylindrical coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from rectangular coordinates to cylindrical coordinates.A)
e. b. f. c. g. d. h. Question
Convert 
from cylindrical coordinates to rectangular coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from cylindrical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Question
Convert 
from rectangular coordinates to cylindrical coordinates.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
from rectangular coordinates to cylindrical coordinates.A)
e. b. f. c. g. d. h. Question
If 
in rectangular coordinates, find the spherical coordinates of P.
in rectangular coordinates, find the spherical coordinates of P. Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Describe the surface whose equation in cylindrical coordinates is 
= 3.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
= 3.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Negative z-axis
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Positive z-axis
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Negative z-axis
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Positive z-axis
H)Cone or half-cone with horizontal axis
Question
Question
Describe the surface whose equation in cylindrical coordinates is 
.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
Question
Question
Find the set of intersection of the surfaces whose equations in spherical coordinates are 
and 
.
and . Question
Question
Find the set of intersection of the surfaces whose equations in spherical coordinates are 
and 
.
and . Question
Describe the surface whose equation in cylindrical coordinates is 
.
. Question
Describe the surface whose equation in spherical coordinates is 
.
. Question
Let A, B, and C be three points on the unit sphere centered at the origin whose spherical coordinates are A = (1, 0, 0), B = 
, and C = 
.(a) Find the angle between 
and 
.(b) Find the angle between 
and 
.(c) Find the angle between 
and 
.
, and C = .(a) Find the angle between and .(b) Find the angle between and .(c) Find the angle between and . Question
Describe the surface whose equation in cylindrical coordinates is 
.
. Question
Find rectangular and spherical equations for the surface whose equation in cylindrical coordinates is 
. Describe the surface.
. Describe the surface. Question
Find the set of intersection of the surfaces whose equations in spherical coordinates are 
and 
.
and . Question
Sketch the solid given in cylindrical coordinates by 
. 
. Question
Sketch the solid given in spherical coordinates by 
. 
. Question
Find the set of intersection of the surfaces whose equations in spherical coordinates are 
and 
.
and . Question
Find rectangular and cylindrical equations for the surface whose equation in spherical coordinates is 
. Describe the surface.
. Describe the surface. Question
Find the set of intersection of the surfaces whose equations in spherical coordinates are 
and 
.
and . Question
Question
Describe in words or sketch the solid represented in cylindrical coordinates by the inequalities 
. 
. Question
Question
Convert the point 
to cylindrical and spherical coordinates.
to cylindrical and spherical coordinates. Question
Describe in words the solid represented in spherical coordinates by the inequality 
.
. Question
Identify the trace of the surface 
in the plane z = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane z = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane x = y.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = y.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Given points A = 
and B = 
in spherical coordinates, find the distance between the two points.
and B = in spherical coordinates, find the distance between the two points. Question
Given points A = 
and B = 
in cylindrical coordinates, find the distance between the two points.
and B = in cylindrical coordinates, find the distance between the two points. Question
Identify the trace of the surface 
in the plane x = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)hyperbolic paraboloid
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)hyperbolic paraboloid
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the trace of the surface 
in the plane z = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane x = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane x = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane y = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane y = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the trace of the surface 
in the plane x = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the surface 
.
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Question
Identify the trace of the surface 
in the plane y = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane y = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Question
Let f(x, y) = 
. If x = 1, find f(x, 2x).
A)1
E)8
B)2
F)9
C)3
G)16
D)4
H)27
. If x = 1, find f(x, 2x).A)1
E)8
B)2
F)9
C)3
G)16
D)4
H)27
Question
Sketch and identify the quadric surface given by 
. 
. Question
Find the range of the function f(x, y) = 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
.A)
e. b. f. c. g. d. h. Question
Find the domain of the function f(x, y) = 
.
A)All points on or to the left of
e.All points on or to the left of x = 0
B)All points on or to the right of
f.All points on or to the right of x = 0
C)All points to the left of
g.All points to the left of x = 0
D)All points to the right of
h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Question
Describe the trace of the surface z = 
= 0 in the plane z = 1.
= 0 in the plane z = 1. Question
Find the coordinates of the point(s) of intersection of the line x = 1 - t, y = 1 - t, z = 4t and the surface z = 
.
. Question
Let f(x, y) = 
. If x = 2, find f(x, 2x).
A)12
E)32
B)16
F)36
C)24
G)42
D)28
H)48
. If x = 2, find f(x, 2x).A)12
E)32
B)16
F)36
C)24
G)42
D)28
H)48
Question
Let S be the quadric surface given by 
. What kind of surface is S?
. What kind of surface is S? Question
Let f(x, y) = x sin y. If x = 
, find f(x, x/2).
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
, find f(x, x/2).A)
e. b. f. c. g. d. h. Question
Find the domain of the function f(x, y) = 
.
A)All points on or to the left of
e.All points on or to the left of x = 0
B)All points on or to the right of
f.All points on or to the right of x = 0
C)All points to the left of
g.All points to the left of x = 0
D)All points to the right of
h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Question
Find the range of the function f(x, y) = 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
.A)
e. b. f. c. g. d. h. Question
Find the range of the function f(x, y) = 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
.A)
e. b. f. c. g. d. h. Question
Let S be the quadric surface given by 
. What are the traces of S in each of the three coordinate planes?
. What are the traces of S in each of the three coordinate planes? Question
Which of the following is not a quadric surface?
A)
d. 
b. 
e. 
c. 
A)
d. b. e. c. Question
Let f(x, y) = x sin y. Find f 
.
A)
e. 
b. 
f. 
c. 
g.1
D)
h.0
.A)
e. b. f. c. g.1D)
h.0 Question
Identify the graph of the function f(x, y) = 
.
A)Cone
E)Hyperboloid of two sheets
B)Paraboloid
F)Hyperbolic cylinder
C)Ellipsoid
G)Elliptic cylinder
D)Hyperboloid of one sheet
H)Parabolic cylinder
.A)Cone
E)Hyperboloid of two sheets
B)Paraboloid
F)Hyperbolic cylinder
C)Ellipsoid
G)Elliptic cylinder
D)Hyperboloid of one sheet
H)Parabolic cylinder
Question
Sketch the graph of 
in 
, and name the surface. 
in , and name the surface. Question
Find the domain of the function f(x, y) = 
.
A)All points on or to the left of
e.All points on or to the left of x = 0
B)All points on or to the right of
f.All points on or to the right of x = 0
C)All points to the left of
g.All points to the left of x = 0
D)All points to the right of
h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Question
Sketch the graph of 
in 
, and name the surface. 
in , and name the surface. Question
Describe the vertical traces x = 0 and the horizontal traces z = -1 (if any) for the surfaces 
and 
.
and .
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Deck 9: Vectors and the Geometry of Space
1
Describe the surface whose equation in cylindrical coordinates is r = 3.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
A
2
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
F
3
If in cylindrical coordinates, find rectangular coordinates of Q.
in cylindrical coordinates, find rectangular coordinates of Q.(0, 1, 3)
4
Convert from spherical coordinates to rectangular coordinates.
A) e. b. f. c. g. d. h.
from spherical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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5
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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6
Convert from rectangular coordinates to spherical coordinates.
A) e. b. f. c. g. d. h.
from rectangular coordinates to spherical coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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7
Convert from cylindrical coordinates to rectangular coordinates.
A) e. b. f. c. g. d. h.
from cylindrical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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8
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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9
Convert from spherical coordinates to rectangular coordinates.
A) e. b. f. c. g. d. h.
from spherical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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10
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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11
Convert from rectangular coordinates to spherical coordinates.
A) e. b. f. c. g. d. h.
from rectangular coordinates to spherical coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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12
Convert from rectangular coordinates to cylindrical coordinates.
A) e. b. f. c. g. d. h.
from rectangular coordinates to cylindrical coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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13
Convert from cylindrical coordinates to rectangular coordinates.
A) e. b. f. c. g. d. h.
from cylindrical coordinates to rectangular coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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14
Convert from rectangular coordinates to cylindrical coordinates.
A) e. b. f. c. g. d. h.
from rectangular coordinates to cylindrical coordinates.A)
e. b. f. c. g. d. h. Unlock Deck
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15
If in rectangular coordinates, find the spherical coordinates of P.
in rectangular coordinates, find the spherical coordinates of P. Unlock Deck
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16
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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17
Describe the surface whose equation in cylindrical coordinates is = 3.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
= 3.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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18
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Negative z-axis
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Positive z-axis
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Negative z-axis
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Positive z-axis
H)Cone or half-cone with horizontal axis
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19
Describe the surface whose equation in cylindrical coordinates is z = 3.
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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20
Describe the surface whose equation in cylindrical coordinates is .
A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
.A)Cylinder with vertical axis
E)Horizontal plane or half-plane
B)Cylinder with horizontal axis
F)Paraboloid
C)Sphere
G)Cone or half-cone with vertical axis
D)Vertical plane or half-plane
H)Cone or half-cone with horizontal axis
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21
Convert the point (0, -5, 0) to cylindrical and spherical coordinates.
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22
Find the set of intersection of the surfaces whose equations in spherical coordinates are and .
and . Unlock Deck
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23
Find cylindrical and spherical equations for the surface whose equation in rectangular coordinates is x = 2. Describe the surface.
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24
Find the set of intersection of the surfaces whose equations in spherical coordinates are and .
and . Unlock Deck
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25
Describe the surface whose equation in cylindrical coordinates is .
. Unlock Deck
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26
Describe the surface whose equation in spherical coordinates is .
. Unlock Deck
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27
Let A, B, and C be three points on the unit sphere centered at the origin whose spherical coordinates are A = (1, 0, 0), B = , and C = .(a) Find the angle between and .(b) Find the angle between and .(c) Find the angle between and .
, and C = .(a) Find the angle between and .(b) Find the angle between and .(c) Find the angle between and . Unlock Deck
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28
Describe the surface whose equation in cylindrical coordinates is .
. Unlock Deck
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29
Find rectangular and spherical equations for the surface whose equation in cylindrical coordinates is . Describe the surface.
. Describe the surface. Unlock Deck
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30
Find the set of intersection of the surfaces whose equations in spherical coordinates are and .
and . Unlock Deck
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31
Sketch the solid given in cylindrical coordinates by .
. Unlock Deck
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32
Sketch the solid given in spherical coordinates by .
. Unlock Deck
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33
Find the set of intersection of the surfaces whose equations in spherical coordinates are and .
and . Unlock Deck
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34
Find rectangular and cylindrical equations for the surface whose equation in spherical coordinates is . Describe the surface.
. Describe the surface. Unlock Deck
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35
Find the set of intersection of the surfaces whose equations in spherical coordinates are and .
and . Unlock Deck
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36
New Orleans is situated at latitude 30° N and longitude 90° W, and New York is situated at latitude 41° N and longitude 74° W. Find the distance from New Orleans to New York, assuming that the radius of the earth is 3960 miles.
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37
Describe in words or sketch the solid represented in cylindrical coordinates by the inequalities .
. Unlock Deck
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38
Use the given data:
Los Angeles: Latitude 34.05°N and Longitude 118.25°W;
Hawaii: Latitude 21.3°N and Longitude 157.83°W.Find the distance from Los Angeles to Hawaii (Assume the radius of earth is 3960 miles.)
Los Angeles: Latitude 34.05°N and Longitude 118.25°W;
Hawaii: Latitude 21.3°N and Longitude 157.83°W.Find the distance from Los Angeles to Hawaii (Assume the radius of earth is 3960 miles.)
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39
Convert the point to cylindrical and spherical coordinates.
to cylindrical and spherical coordinates. Unlock Deck
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40
Describe in words the solid represented in spherical coordinates by the inequality .
. Unlock Deck
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41
Identify the trace of the surface in the plane z = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
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42
Identify the trace of the surface in the plane z = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
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43
Identify the trace of the surface in the plane x = y.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = y.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
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44
Given points A = and B = in spherical coordinates, find the distance between the two points.
and B = in spherical coordinates, find the distance between the two points. Unlock Deck
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45
Given points A = and B = in cylindrical coordinates, find the distance between the two points.
and B = in cylindrical coordinates, find the distance between the two points. Unlock Deck
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46
Identify the trace of the surface in the plane x = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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k this deck
47
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)hyperbolic paraboloid
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)hyperbolic paraboloid
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48
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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k this deck
49
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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k this deck
50
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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k this deck
51
Identify the trace of the surface in the plane z = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane z = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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k this deck
52
Identify the trace of the surface in the plane x = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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k this deck
53
Identify the trace of the surface in the plane x = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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k this deck
54
Identify the trace of the surface in the plane y = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane y = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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k this deck
55
Identify the trace of the surface in the plane x = 1.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane x = 1.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
Unlock Deck
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Unlock Deck
k this deck
56
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
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k this deck
57
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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Unlock Deck
k this deck
58
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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Unlock Deck
k this deck
59
Identify the surface .
A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
.A)ellipsoid but not a sphere
E)sphere
B)hyperboloid of one sheet
F)elliptic but not circular paraboloid
C)hyperboloid of two sheets
G)cone
D)cylinder
H)circular paraboloid (figure of revolution)
Unlock Deck
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k this deck
60
Identify the trace of the surface in the plane y = 0.
A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
in the plane y = 0.A)ellipse but not a circle
E)two parallel straight lines
B)parabola
F)two intersecting straight lines
C)hyperbola
G)point
D)circle
H)straight line
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61
Let f(x, y) = . If x = 1, find f(x, 2x).
A)1
E)8
B)2
F)9
C)3
G)16
D)4
H)27
. If x = 1, find f(x, 2x).A)1
E)8
B)2
F)9
C)3
G)16
D)4
H)27
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62
Sketch and identify the quadric surface given by .
. Unlock Deck
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63
Find the range of the function f(x, y) = .
A) e. b. f. c. g. d. h.
.A)
e. b. f. c. g. d. h. Unlock Deck
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64
Find the domain of the function f(x, y) = .
A)All points on or to the left of e.All points on or to the left of x = 0
B)All points on or to the right of f.All points on or to the right of x = 0
C)All points to the left of g.All points to the left of x = 0
D)All points to the right of h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Unlock Deck
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65
Describe the trace of the surface z = = 0 in the plane z = 1.
= 0 in the plane z = 1. Unlock Deck
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66
Find the coordinates of the point(s) of intersection of the line x = 1 - t, y = 1 - t, z = 4t and the surface z = .
. Unlock Deck
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67
Let f(x, y) = . If x = 2, find f(x, 2x).
A)12
E)32
B)16
F)36
C)24
G)42
D)28
H)48
. If x = 2, find f(x, 2x).A)12
E)32
B)16
F)36
C)24
G)42
D)28
H)48
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68
Let S be the quadric surface given by . What kind of surface is S?
. What kind of surface is S? Unlock Deck
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69
Let f(x, y) = x sin y. If x = , find f(x, x/2).
A) e. b. f. c. g. d. h.
, find f(x, x/2).A)
e. b. f. c. g. d. h. Unlock Deck
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70
Find the domain of the function f(x, y) = .
A)All points on or to the left of e.All points on or to the left of x = 0
B)All points on or to the right of f.All points on or to the right of x = 0
C)All points to the left of g.All points to the left of x = 0
D)All points to the right of h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Unlock Deck
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71
Find the range of the function f(x, y) = .
A) e. b. f. c. g. d. h.
.A)
e. b. f. c. g. d. h. Unlock Deck
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72
Find the range of the function f(x, y) = .
A) e. b. f. c. g. d. h.
.A)
e. b. f. c. g. d. h. Unlock Deck
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73
Let S be the quadric surface given by . What are the traces of S in each of the three coordinate planes?
. What are the traces of S in each of the three coordinate planes? Unlock Deck
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74
Which of the following is not a quadric surface?
A) d. b. e. c.
A)
d. b. e. c. Unlock Deck
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75
Let f(x, y) = x sin y. Find f .
A) e. b. f. c. g.1
D) h.0
.A)
e. b. f. c. g.1D)
h.0 Unlock Deck
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76
Identify the graph of the function f(x, y) = .
A)Cone
E)Hyperboloid of two sheets
B)Paraboloid
F)Hyperbolic cylinder
C)Ellipsoid
G)Elliptic cylinder
D)Hyperboloid of one sheet
H)Parabolic cylinder
.A)Cone
E)Hyperboloid of two sheets
B)Paraboloid
F)Hyperbolic cylinder
C)Ellipsoid
G)Elliptic cylinder
D)Hyperboloid of one sheet
H)Parabolic cylinder
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77
Sketch the graph of in , and name the surface.
in , and name the surface. Unlock Deck
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78
Find the domain of the function f(x, y) = .
A)All points on or to the left of e.All points on or to the left of x = 0
B)All points on or to the right of f.All points on or to the right of x = 0
C)All points to the left of g.All points to the left of x = 0
D)All points to the right of h.All points in the xy-plane
.A)All points on or to the left of
e.All points on or to the left of x = 0B)All points on or to the right of
f.All points on or to the right of x = 0C)All points to the left of
g.All points to the left of x = 0D)All points to the right of
h.All points in the xy-plane Unlock Deck
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79
Sketch the graph of in , and name the surface.
in , and name the surface. Unlock Deck
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80
Describe the vertical traces x = 0 and the horizontal traces z = -1 (if any) for the surfaces and .
and . Unlock Deck
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k this deck
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Unlock for access to all 269 flashcards in this deck.
