Deck 15: Section 5: Vector Analysis

Question 1

Identify the surface by eliminating the parameters from the vector-valued function .

A) plane
B) sphere
C) paraboloid
D) cylinder
E) ellipsoid

Answer 1

ellipsoid

Question 2

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone, where .

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function and sketch the graph.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find a vector-valued function whose graph is the plane .

A)
B)
C)
D)
E)

Question 5

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere,

A)
B)
C)
D)
E)

Question 6

Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.

A)
B)
C)
D)
E)

Question 7

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.

A)
B)
C)
D)
E)

Question 8

Match the following vector-valued function with its graph.

A)
B)
C)
D)
E)

Question 9

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the x-axis.

A)
B)
C)
D)
E)

Question 10

Match the following vector-valued function with its graph.

A)
B)
C)
D)
E)

Question 11

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function .

A)
B)
C)
D)
E)

Question 12

Find the area of the surface given by , where .

A)
B)
C)
D)
E)

Question 13

Find the area of the surface of revolution .

A)
B)
C)
D)
E)

Question 14

Find a vector-valued function whose graph is the ellipsoid .

A)
B)
C)
D)
E)

Question 15

Find a vector-valued function whose graph is the cone .

A)
B)
C)
D)
E)

Question 16

Find a vector-valued function whose graph is the part of the paraboloid that lies inside the cylinder .

A)
B)
C)
D)
E)

Question 17

Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.

A)
B)
C)
D)
E)

Question 18

The surface of the dome on a new museum is given by and is in meters. Find the surface area of the dome.

A)
B)
C)
D)
E)

Question 19

Find a vector-valued function for the hyperboloid .

A)
B)
C)
D)
E)

Question 20

Find a vector-valued function whose graph is the cylinder .

A)
B)
C)
D)
E)

Question 21

Determine the tangent plane for the hyperboloid .

A)
B)
C)
D)
E)