Question 1

Find the vectors   for the following vector function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    B

Question 2

A particle moves in the yz-plane along the curve represented by the vector-valued function   Find the maximum value of

Accepted Answer

A) 4 
B) 3 
C) 7 
D) 8 
E) 5 
A) 4 
B) 3 
C) 7 
D) 8 
E) 5 C

Question 3

Use the properties of the derivative to find   given the following vector-valued functions.

Accepted Answer

A) 2 
B)    
C)    
D) 5 
E)    
A) 2 
B)    
C)    
D) 5 
E)    E

Question 4

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Given the vector-valued function below, evaluate

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find   given the following vector function:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the domain of the vector-valued function given below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Find the indefinite integral below.   Do not include an arbitrary constant vector.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Use the properties of the derivative to find   given the following vector-valued functions.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Use the properties of the derivative to find   given the following vector-valued functions.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Determine the interval on which the vector-valued function   s continuous.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find   given the following vector function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

given the following vector function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

given the following.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Represent the following curve by a vector-valued function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find   given the following vector function.

Accepted Answer

A) cost sint 
B)    
C)    
D) -16 sin t cos t 
E)    
A) cost sint 
B)    
C)    
D) -16 sin t cos t 
E)

Question 19

A particle moves in the yz-plane along the curve represented by the vector-valued function   Find the minimum value of

Accepted Answer

A) 6 
B) 4 
C) 7 
D) 9 
E) 8 
A) 6 
B) 4 
C) 7 
D) 9 
E) 8

Question 20

Find the indefinite integral below.   Do not include an arbitrary constant vector.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the vectors for the following vector function.

A particle moves in the yz-plane along the curve represented by the vector-valued function Find the maximum value of

Use the properties of the derivative to find given the following vector-valued functions.

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.

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below.

Given the vector-valued function below, evaluate

Find given the following vector function:

Find the domain of the vector-valued function given below.

Find the indefinite integral below. Do not include an arbitrary constant vector.

Use the properties of the derivative to find given the following vector-valued functions.

Use the properties of the derivative to find given the following vector-valued functions.

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.

Determine the interval on which the vector-valued function s continuous.

Find given the following vector function.

given the following vector function.

given the following.

Represent the following curve by a vector-valued function.

Find given the following vector function.

A particle moves in the yz-plane along the curve represented by the vector-valued function Find the minimum value of

Find the indefinite integral below. Do not include an arbitrary constant vector.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

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Exam 12: Vector-Valued Functions

Find the vectors for the following vector function.

A particle moves in the yz-plane along the curve represented by the vector-valued function Find the maximum value of

Use the properties of the derivative to find given the following vector-valued functions.

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.

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below.

Given the vector-valued function below, evaluate

Find given the following vector function:

Find the domain of the vector-valued function given below.

Find the indefinite integral below. Do not include an arbitrary constant vector.

Use the properties of the derivative to find given the following vector-valued functions.

Use the properties of the derivative to find given the following vector-valued functions.

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.

Determine the interval on which the vector-valued function s continuous.

Find given the following vector function.

given the following vector function.

given the following.

Represent the following curve by a vector-valued function.

Find given the following vector function.

A particle moves in the yz-plane along the curve represented by the vector-valued function Find the minimum value of

Find the indefinite integral below. Do not include an arbitrary constant vector.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters