731 Chapter 12: Vector-Valued Functions
12.1 Vector-Valued Functions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the domain of the vector-valued function given below.
a.
b.
c.
d.
e.
____ 2. Find the domain of the vector-valued function given below.
a.
b.
c.
d.
e.
____ 3. Given the vector-valued function below, evaluate .
a.
b.
12.1 Vector-Valued Functions
732
c.
d.
e.
____ 4. Find given the functions below.
a.
b.
c.
d.
e.
____ 5. Match the equation with the graph shown in red below.
733 Chapter 12: Vector-Valued Functions
a.
b.
c.
d.
e.
____ 6. The graph below is most likely the graph of which of the following equations?
a.
b.
c.
d.
e.
12.1 Vector-Valued Functions 734
____ 7. Sketch the curve represented by the vector-valued function and
give the orientation of the curve.
a. d.
b. e.
c.
735
Chapter 12: Vector-Valued Functions
____
8.
Sketch the curve represented by the vector-valued function
and give the orientation of the curve.
a.
d.
b. e.
c.
12.1 Vector-Valued Functions
736
____ 9. Represent the following curve by a vector-valued function.
a.
b.
c.
d.
e.
____ 10. Find a vector-valued function, using the given parameter, to represent the intersection
of the surfaces given below.
Surfaces Parameter
a.
b.
c.
d.
e.
737
Chapter 12: Vector-Valued Functions
____
11.
of the surfaces given below.
Surfaces
a.
b.
c.
d.
e.
____
12.
of the surfaces given below.
Surfaces
a.
b.
c.
d.
e.
____
13.
of the surfaces given below.
Surfaces
a.
b.
c.
12.1 Vector-Valued Functions
738
d.
e.
____ 14. Evaluate the limit given below.
The limit does not exist.
____ 15. Evaluate the limit given below.
The limit does not exist.
739 Chapter 12: Vector-Valued Functions
____ 16. Determine the interval on which the vector-valued function
is continuous.
a.
b.
c.
d.
e.
____ 17. Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5
meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom.
Find a vector-valued function for the helix.
a.
b.
c.
d.
e.
____ 18. Suppose the two particles travel along the space curves
and . A collision will occur at the
point of intersection P if both particles are at P at the same time. Find the point of collision.
a.
b.
c.
d.
e.
12.1 Vector-Valued Functions
740
12.1 Vector-Valued Functions
Answer Section
741 Chapter 12: Vector-Valued Functions
12.2 Differentiation and Integration of Vector-Values Functions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the vectors and for the following vector function.
a.
b.
c.
d.
e.
____ 2. Find given the following vector function.
a.
b.
c.
d.
e.
____ 3. Find given the following vector function.
a.
b.
c.
d.
e.
12.2 Differentiation and Integration of Vector-Valued Functions
742
____ 4. Find given the following vector function.
a.
b.
c.
d.
e.
____ 5. Find given the following vector function:
a.
b.
c.
d.
e.
____ 6. Find given the following vector function.
a.
b.
c.
d.
e.
743 Chapter 12: Vector-Valued Functions
____ 7. Find given the following vector function.
cost sint
–34
34
–16 sin t cos t
3
____
8.
Find the open interval on which the curve given by the vector-valued function
is smooth.
a.
b.
c.
d.
e.
____
9.
Use the properties of the derivative to find
given the following
vector-valued functions.
a.
b.
c.
d.
e.
____ 10. Use the properties of the derivative to find given the following
vector-valued functions.
a.
b.
c.
12.2 Differentiation and Integration of Vector-Valued Functions
744
d.
e.
____ 11. Use the properties of the derivative to find given the following
vector-valued functions.
a.
b.
c.
d.
e.
____ 12. Use the properties of the derivative to find given the following
vector-valued functions.
2
5
745 Chapter 12: Vector-Valued Functions
____ 13. Use the properties of the derivative to find given the following vector-
valued functions.
a.
b.
c.
d.
e.
____ 14. Find the indefinite integral below.
Do not include an arbitrary constant vector.
a.
b.
c.
d.
e.
12.2 Differentiation and Integration of Vector-Valued Functions
746
____ 15. Find the indefinite integral below.
Do not include an arbitrary constant vector.
a.
b.
c.
d.
e.
____ 16. Evaluate the definite integral below.
a.
b.
c.
d.
e.
____ 17. Find given the following.
a.
b.
c.
d.
e.
747 Chapter 12: Vector-Valued Functions
____ 18. A particle moves in the yz– plane along the curve represented by the vector-valued
function . Find the minimum value of .
6
4
7
9
8
____ 19. A particle moves in the yz– plane along the curve represented by the vector-valued
function . Find the maximum value of .
4
3
7
8
5
12.2 Differentiation and Integration of Vector-Valued Functions
748
12.2 Differentiation and Integration of Vector-Values Functions
Answer Section
749 Chapter 12: Vector-Valued Functions
12.3 Velocity and Acceleration
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. The position vector describes the path of an object moving in the xy-plane. Sketch a graph
of the path and sketch the velocity and acceleration vectors at the point
.
a. d.
b. e.