Deck 12: Vector-Valued Functions

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

Given the vector-valued function below, evaluate

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A)
B)
C)
D)
E)

Question 5

Represent the following curve by a vector-valued function.

A)
B)
C)
D)
E)

Question 6

The graph below is most likely the graph of which of the following equations?

A)
B)
C)
D)
E)

Question 7

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

A)
B)
C)
D)
E)

Question 8

Evaluate the limit given below.

A)
B)
C)
D)
E)The limit does not exist.

Question 9

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

A)
B)
C)
D)
E)

Question 10

given the following vector function.

A)
B)
C)
D)
E)

Question 11

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)

Question 12

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

A)
B)
C)
D)
E)

Question 13

Find the vectors for the following vector function.

A)
B)
C)
D)
E)

Question 14

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)

Question 15

given the functions below.

A)
B)
C)
D)
E)

Question 16

Evaluate the limit given below.

A)
B)
C)
D)
E)The limit does not exist.

Question 17

Match the equation with the graph shown in red below.

A)
B)
C)
D)
E)

Question 18

Sketch the curve represented by the vector-valued function and give the orientation of the curve.

A)
B)
C)
D)
E)

Question 19

Sketch the curve represented by the vector-valued function give the orientation of the curve.

A)
B)
C)
D)
E)

Question 20

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

A)
B)
C)
D)
E)

Question 21

Find given the following vector function:

A)
B)
C)
D)
E)

Question 22

Find given the following vector function.

A)
B)
C)
D)
E)

Question 23

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

A)
B)
C)
D)
E)

Question 24

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

A)
B)
C)
D)
E)

Question 25

Find given the following vector function.

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

Question 26

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

A)
B)
C)
D)
E)

Question 27

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

A)
B)
C)
D)
E)

Question 28

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

Question 29

Find the open interval on which the curve given by the vector-valued function is smooth.

A)
B)
C)
D)
E)

Question 30

Find given the following vector function.

A)
B)
C)
D)
E)

Question 31

given the following vector function.

A)
B)
C)
D)
E)

Question 32

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

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

Question 33

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

A)
B)
C)
D)
E)

Question 34

Evaluate the definite integral below.

A)
B)
C)
D)
E)

Question 35

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

Question 36

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

A)
B)
C)
D)
E)

Question 37

given the following.

A)
B)
C)
D)
E)