Digital Test Bank - Calculus Concepts and Contexts,Stewart,5e

10.1 Vector Functions and Space Curves

1. Find the limit.




a. r(t) = 4k
b. r(t) = 4j
c. r(t) = 4i – 3k
d. r(t) = 4i + 12j + 3k
e. r(t) = 4i
ANSWER: e
POINTS: 1
DIFFICULTY: Medium
REFERENCES: 13.1.3
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.LO.11.01.05 - Find the limit of a vector-valued function.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:04 AM




2. Let r(t) = .

Find the domain of r.

a. (–1, 8]
b. (–1, 0) ∪ (0, 8]
c. (8, ∞]
d. (–∞, –1)
e. [8, 0) ∪(0, 2)
ANSWER: b
POINTS: 1
DIFFICULTY: Medium
REFERENCES: 13.1.1
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.UO.11.01 - Analyze vector functions and space curves.
OTHER: Bimodal
NOTES: Section 13.1
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,10.1 Vector Functions and Space Curves

DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:05 AM



3. Find the domain of the vector function r(t) = 4ti + j.

a. (–∞, – 9)∪(– 9, ∞)
b. (–∞, 4)∪(4, ∞)
c. (– ∞, –4)∪(– 4, ∞)
d. (–∞, 9)∪(9, ∞)
ANSWER: d
POINTS: 1
DIFFICULTY: Easy
REFERENCES: 13.1.2
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.UO.11.01 - Analyze vector functions and space curves.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:07 AM



4. Find the domain of the vector function r(t) = .

a.
b.
c.
d.
ANSWER: b
POINTS: 1
DIFFICULTY: Medium
REFERENCES: 13.1.1
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.UO.11.01 - Analyze vector functions and space curves.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:08 AM

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,10.1 Vector Functions and Space Curves


5. Find the limit .

a. 5i – 3k
b. 6i + j
c. 5i + j – 3k
d. 6i
ANSWER: c
POINTS: 1
DIFFICULTY: Easy
REFERENCES: 13.1.3
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.LO.11.01.05 - Find the limit of a vector-valued function.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:09 AM

6. Find a vector function that represents the curve of intersection of the two surfaces:

the top half of the ellipsoid x2 + 4y2 + 4z2 = 16 and the parabolic cylinder y = x2.

a.



b.



c.



d.



e.



ANSWER: a
POINTS: 1
DIFFICULTY: Medium
REFERENCES: 13.1.44
QUESTION TYPE: Multi-Mode (Multiple choice)
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, 10.1 Vector Functions and Space Curves

HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.UO.11.01 - Analyze vector functions and space curves.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 2/18/2020 5:11 AM

7. Find a vector function that represents the curve of intersection of the two surfaces:

The circular cylinder x2 + y2 = 9 and the parabolic cylinder z = xy.

a. r(t) = costi + sintj – 9cos2tk
b. r(t) = 3cos(t)i + 3sin(t)j + 9sin(t)cos(t)k
c. r(t) = 3cos(t)i + 3sin(t)j – sin(t)cos(t)k
d. r(t) = cos(t)i + sin(t)j + 9sin(t)cos(t)k
e. r(t) = 9cos(t)i + 9tj + 9cos2tk
ANSWER: b
POINTS: 1
DIFFICULTY: Medium
REFERENCES: 13.1.40
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: CALC.COH.UO.11.01 - Analyze vector functions and space curves.
OTHER: Bimodal
NOTES: Section 13.1
DATE CREATED: 7/20/2015 2:32 PM
DATE MODIFIED: 7/20/2015 2:32 PM

8. Find the following limit.




ANSWER:




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