Larson_Calculus_10e ch15sec05
MULTIPLE CHOICE
1. Match the following vector-valued function with its graph.
a.
d.
b.
e.
c.
2. Match the following vector-valued function with its graph.
a.
d.
b.
e.
c.
3. Find the rectangular equation for the surface by eliminating parameters from the vector-valued
function. Identify the surface.
a.
b.
c.
d.
e.
4. Find the rectangular equation for the surface by eliminating the parameters from the vector-valued
function .
a.
b.
c.
d.
e.
5. Identify the surface by eliminating the parameters from the vector-valued function
.
a.
plane
b.
sphere
c.
paraboloid
d.
cylinder
e.
ellipsoid
6. Find the rectangular equation for the surface by eliminating the parameters from the vector-valued
function and sketch the graph.
a.
d.
b.
e.
c.
7. Find a vector-valued function whose graph is the plane .
a.
b.
c.
d.
e.
8. Find a vector-valued function whose graph is the cone .
a.
b.
c.
d.
e.
9. Find a vector-valued function whose graph is the cylinder .
a.
b.
c.
d.
e.
10. Find a vector-valued function whose graph is the ellipsoid .
a.
b.
c.
d.
e.
11. Find a vector-valued function whose graph is the ellipsoid .
a.
b.
c.
d.
e.
12. Find a vector-valued function whose graph is the part of the paraboloid that lies inside the
cylinder .
a.
b.
c.
d.
e.
13. 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.
14. 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.
15. 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.
16. Find the area of the surface given by , where .
a.
b.
c.
d.
e.
17. 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.
18. 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.
19. Find the area of the surface of revolution
.
a.
b.
c.
d.
e.
20. 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.
21. Find a vector-valued function for the hyperboloid .
a.
b.
c.
d.
e.
22. Determine the tangent plane for the hyperboloid .
a.
b.
c.
d.
e.