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12.1 Vector-Valued Functions 703
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.
704 Chapter 12: Vector-Valued Functions
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.
12.1 Vector-Valued Functions 705
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.
706 Chapter 12: Vector-Valued Functions
____ 7. 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 707
____ 8. Sketch the curve represented by the vector-valued function
and give the orientation of the curve.
a. d.
b. e.
c.
708 Chapter 12: Vector-Valued Functions
____ 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.
12.1 Vector-Valued Functions 709
____ 11. 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.
____ 12. 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.
____ 13. Find a vector-valued function, using the given parameter, to represent the intersection
of the surfaces given below.
Surfaces Parameter
a.
b.
c.
710 Chapter 12: Vector-Valued Functions
d.
e.
____ 14. Evaluate the limit given below.
a.
b.
c.
d.
e. The limit does not exist.
____ 15. Evaluate the limit given below.
a.
b.
c.
d.
e. The limit does not exist.
12.1 Vector-Valued Functions 711
____ 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.
712 Chapter 12: Vector-Valued Functions
12.1 Vector-Valued Functions
Answer Section
