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12.2 Differentiation and Integration of Vector-Valued Functions 713
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.
714 Chapter 12: Vector-Valued Functions
____ 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.
12.2 Differentiation and Integration of Vector-Valued Functions 715
____ 7. Find given the following vector function.
a. cost sint
b. –34
c. 34
d. –16 sin t cos t
e. 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.
716 Chapter 12: Vector-Valued Functions
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.
a. 2
b.
c.
d. 5
e.
12.2 Differentiation and Integration of Vector-Valued Functions 717
____ 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.
718 Chapter 12: Vector-Valued Functions
____ 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.
12.2 Differentiation and Integration of Vector-Valued Functions 719
____ 18. A particle moves in the yz-plane along the curve represented by the vector-valued
function . Find the minimum value of .
a. 6
b. 4
c. 7
d. 9
e. 8
____ 19. A particle moves in the yz-plane along the curve represented by the vector-valued
function . Find the maximum value of .
a. 4
b. 3
c. 7
d. 8
e. 5
720 Chapter 12: Vector-Valued Functions
12.2 Differentiation and Integration of Vector-Values Functions
Answer Section
