Question 1

Compute the arc length.

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find a parametric representation of the surface.

Accepted Answer

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

Question 4

At Erik's sixth-year birthday party, the children are playing a game where each contestant tries to throw a tennis ball into a cardboard box located 19 feet away. The box is 24 inches tall and 15 inches wide (see figure). A child tosses a ball with an initial height of 14 inches and an angle of 60o from the horizontal. If the initial speed of the ball is 25 feet per second, will the ball land in the box? Show all of your work. [Ignore the radius of the ball. Assume that the only force acting on the ball is gravity.Assume that the ball is "on-target" and that there is nothing behind the box to cause a rebound. Note that g = 32 ft/s2 = 384 in/s2.]     blank
blank
24 inches
19 feet
15 inches
[The figure not necessarily drawn to scale.]

Accepted Answer

For convenience, convert all distances t

Question 5

Find the limit if it exists.

Accepted Answer

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

Question 6

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 7

A projectile is fired with initial speed   feet per second from a height of h feet at an angle of   above the horizontal. Assuming that the only force acting on the object is gravity, find the horizontal range. Round to the nearest tenth of a foot.

Accepted Answer

A)  928.8 ft 
B)  2131.8 ft 
C)  281.1 ft 
D)  2127.5 ft 
A)  928.8 ft 
B)  2131.8 ft 
C)  281.1 ft 
D)  2127.5 ft

Question 8

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 3.1 rad/s, and the (constant) frictional force stops the wheel in about 2.5 seconds. If the frictional force produces a torque of 19.1 foot-pounds, estimate the moment of inertia of the wheel.

Accepted Answer

A)  15.4 
B)  3.9 
C)  0.0649 
D)  7.1 
A)  15.4 
B)  3.9 
C)  0.0649 
D)  7.1

Question 9

Find all values of t such that   is parallel to the xy-plane.

Accepted Answer

A)    
B)    
C)    
D)    is not parallel to the xy-plane for any real value of t 
A)    
B)    
C)    
D)    is not parallel to the xy-plane for any real value of t

Question 10

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

Accepted Answer

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

Question 11

Find the force acting on an object of mass 9 kg with the given position function (in meters and seconds).

Accepted Answer

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

Question 12

Find the derivative of the given vector-valued function.

Accepted Answer

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

Question 13

Use graphing technology to sketch the curve traced out by the given vector-valued function.

Accepted Answer

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

Question 14

Find the curvature of the polar curve at the indicated point.

Accepted Answer

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

Question 15

Determine whether the following is true or false.

Accepted Answer

Answers may vary.
False. Let @#IMG-DLM& be the ant

Question 16

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

Accepted Answer

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

Question 17

Sketch, by hand, the curve traced out by the given vector-valued function.

Accepted Answer

The answer of Sketch, by hand, the curve traced out...

Question 18

Determine whether the speed of the object is increasing, decreasing, or constant at the given point.

Accepted Answer

A)  increasing 
B)  decreasing 
C)  constant 
A)  increasing 
B)  decreasing 
C)  constant

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 = 115 (slugs) from skidding.

Accepted Answer

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

Question 20

Find parametric equations for the indicated curve.
The intersection of   and x + y = 2

Accepted Answer

Answers may vary. On

Compute the arc length.

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

Find a parametric representation of the surface.

Find the limit if it exists.

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

A projectile is fired with initial speed feet per second from a height of h feet at an angle of above the horizontal. Assuming that the only force acting on the object is gravity, find the horizontal range. Round to the nearest tenth of a foot.

Find all values of t such that is parallel to the xy-plane.

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

Find the force acting on an object of mass 9 kg with the given position function (in meters and seconds).

Find the derivative of the given vector-valued function.

Use graphing technology to sketch the curve traced out by the given vector-valued function.

Find the curvature of the polar curve at the indicated point.

Determine whether the following is true or false.

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

Sketch, by hand, the curve traced out by the given vector-valued function.

Determine whether the speed of the object is increasing, decreasing, or constant at the given point.

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 = 115 (slugs) from skidding.

Find parametric equations for the indicated curve. The intersection of and x + y = 2

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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 13: Vector-Valued Functions

Compute the arc length.

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

Find a parametric representation of the surface.

Find the limit if it exists.

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

A projectile is fired with initial speed feet per second from a height of h feet at an angle of above the horizontal. Assuming that the only force acting on the object is gravity, find the horizontal range. Round to the nearest tenth of a foot.

Find all values of t such that is parallel to the xy-plane.

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

Find the force acting on an object of mass 9 kg with the given position function (in meters and seconds).

Find the derivative of the given vector-valued function.

Use graphing technology to sketch the curve traced out by the given vector-valued function.

Find the curvature of the polar curve at the indicated point.

Determine whether the following is true or false.

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

Sketch, by hand, the curve traced out by the given vector-valued function.

Determine whether the speed of the object is increasing, decreasing, or constant at the given point.

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 = 115 (slugs) from skidding.

Find parametric equations for the indicated curve. The intersection of and x + y = 2

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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