Question 1

Sketch a plausible curve with domain   that has the curvature function graphed below.

Accepted Answer

Answers may vary with respect to the loc

Question 2

Find the force acting on an object of mass 12 kg with the given position function (in meters and seconds).

Accepted Answer

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

Question 3

Find the landing point for a projectile launched under the given conditions. Round distances to the nearest foot. Assign your coordinate system as indicated in the figure below.

Accepted Answer

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

Question 4

Find the unit tangent vector to the curve at the indicated point.

Accepted Answer

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

Question 5

Which of the following is a parametric representation of the given surface?

Accepted Answer

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

Question 6

Sketch the curve and find any points of maximum or minimum curvature.

Accepted Answer

A)  maximum curvature:   ; minimum curvature:   
B)  maximum curvature:   ; minimum curvature:   
C)  maximum curvature:   and   ; no minimum curvature 
D)  maximum curvature:   ; no minimum curvature 
A)  maximum curvature:   ; minimum curvature:   
B)  maximum curvature:   ; minimum curvature:   
C)  maximum curvature:   and   ; no minimum curvature 
D)  maximum curvature:   ; no minimum curvature

Question 7

Find a parametrically-defined vector   that represents the plane with the given properties. The plane through the point   and containing
The vectors   .

Accepted Answer

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

Question 8

Find the limit if it exists.

Accepted Answer

A)    
B)    
C)    
D)  does not exist 
A)    
B)    
C)    
D)  does not exist

Question 9

Match the vector-valued function with its graph.

Accepted Answer

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

Question 10

Sketch the curve and find any points of maximum or minimum curvature.

Accepted Answer

A)  maximum curvature:   and   ; minimum curvature:   
B)  no maximum curvature; minimum curvature:   and   
C)  maximum curvature:   and   ; minimum curvature:   
D)  maximum curvature:   and   ; no minimum curvature 
A)  maximum curvature:   and   ; minimum curvature:   
B)  no maximum curvature; minimum curvature:   and   
C)  maximum curvature:   and   ; minimum curvature:   
D)  maximum curvature:   and   ; no minimum curvature

Question 11

Which of the following is a parametric representation of the given surface?   [Assume the axes are oriented as shown in the figure below.]

Accepted Answer

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

Question 12

Determine all values of t at which the given vector-valued function is continuous.

Accepted Answer

A)    
B)    
C)    
D)  all real numbers 
A)    
B)    
C)    
D)  all real numbers

Question 13

Find the limit if it exists.

Accepted Answer

A)    
B)    
C)    
D)  does not exist 
A)    
B)    
C)    
D)  does not exist

Question 14

A golfer rotates a club with constant angular acceleration   through an angle of   radians. If the angular velocity increases from 0 to 10 rad/sec, find   .

Accepted Answer

A)    rad/sec2 
B)    rad/sec2 
C)    rad/sec2 
D)    rad/sec2 
A)    rad/sec2 
B)    rad/sec2 
C)    rad/sec2 
D)    rad/sec2

Question 15

Which of the following is the graph of the given parametric surface?

Accepted Answer

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

Question 16

Find the curvature at the given point.

Accepted Answer

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

Question 17

On the highly-successful TV game show Wheel of Fortune, a contestant spins a large spinner wheel that determines the amount of money for which the contestant is playing. Typically, contestants spin the wheel at an initial rate of 3.3 rad/s, and the (constant) frictional force stops the wheel in about 2.7 seconds. If the frictional force produces a torque of 19.1 foot-pounds, estimate the moment of inertia of the wheel.

Accepted Answer

A)  15.6 
B)  4.0 
C)  0.0640 
D)  7.2 
A)  15.6 
B)  4.0 
C)  0.0640 
D)  7.2

Question 18

Graph the curvature function   for   and find the limit of the curvature as   .

Accepted Answer

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

Question 19

The friction force required to keep a car from skidding on a curve is given by   . Find the friction force needed to keep a car of mass m = 90 (slugs) from skidding.

Accepted Answer

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

Question 20

Which of the following is an arc length parameterization of the given two-dimensional curve? The circle of radius 4 centered at the origin

Accepted Answer

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

Sketch a plausible curve with domain that has the curvature function graphed below.

Find the force acting on an object of mass 12 kg with the given position function (in meters and seconds).

Find the landing point for a projectile launched under the given conditions. Round distances to the nearest foot. Assign your coordinate system as indicated in the figure below.

Find the unit tangent vector to the curve at the indicated point.

Which of the following is a parametric representation of the given surface?

Sketch the curve and find any points of maximum or minimum curvature.

Find a parametrically-defined vector that represents the plane with the given properties. The plane through the point and containing The vectors .

Find the limit if it exists.

Match the vector-valued function with its graph.

Sketch the curve and find any points of maximum or minimum curvature.

Which of the following is a parametric representation of the given surface? [Assume the axes are oriented as shown in the figure below.]

Determine all values of t at which the given vector-valued function is continuous.

Find the limit if it exists.

A golfer rotates a club with constant angular acceleration through an angle of radians. If the angular velocity increases from 0 to 10 rad/sec, find .

Which of the following is the graph of the given parametric surface?

Find the curvature at the given point.

Graph the curvature function for and find the limit of the curvature as .

The friction force required to keep a car from skidding on a curve is given by . Find the friction force needed to keep a car of mass m = 90 (slugs) from skidding.

Which of the following is an arc length parameterization of the given two-dimensional curve? The circle of radius 4 centered at the origin

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 12: Vector-Valued Functions

Sketch a plausible curve with domain that has the curvature function graphed below.

Find the force acting on an object of mass 12 kg with the given position function (in meters and seconds).

Find the landing point for a projectile launched under the given conditions. Round distances to the nearest foot. Assign your coordinate system as indicated in the figure below.

Find the unit tangent vector to the curve at the indicated point.

Which of the following is a parametric representation of the given surface?

Sketch the curve and find any points of maximum or minimum curvature.

Find a parametrically-defined vector that represents the plane with the given properties. The plane through the point and containing The vectors .

Find the limit if it exists.

Match the vector-valued function with its graph.

Sketch the curve and find any points of maximum or minimum curvature.

Which of the following is a parametric representation of the given surface? [Assume the axes are oriented as shown in the figure below.]

Determine all values of t at which the given vector-valued function is continuous.

Find the limit if it exists.

A golfer rotates a club with constant angular acceleration through an angle of radians. If the angular velocity increases from 0 to 10 rad/sec, find .

Which of the following is the graph of the given parametric surface?

Find the curvature at the given point.

Graph the curvature function for and find the limit of the curvature as .

The friction force required to keep a car from skidding on a curve is given by . Find the friction force needed to keep a car of mass m = 90 (slugs) from skidding.

Which of the following is an arc length parameterization of the given two-dimensional curve? The circle of radius 4 centered at the origin

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters