Question 1

Label the statement as true (i.e., always true) or false and explain your answer. [Assume that T, N, and B are defined.]

Accepted Answer

A) True 
 B)False

Question 2

Find the curvature at the given point.

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Use the graph of   below to predict whether the curvature would be larger at   or   .

Accepted Answer

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

Question 5

Match the vector-valued function with its graph.

Accepted Answer

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

Question 6

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 7

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 8

Identify and sketch a graph of the surface.

Accepted Answer

elliptic p

Question 9

Which of the following is an arc length parameterization of the given two-dimensional curve? The line segment from   to

Accepted Answer

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

Question 10

Use a CAS to estimate the arc length of the curve.

Accepted Answer

A)  17.6 
B)  56.5 
C)  23.5 
D)  7.6 
A)  17.6 
B)  56.5 
C)  23.5 
D)  7.6

Question 11

Find the osculating circle at the given point.

Accepted Answer

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

Question 12

Identify and sketch a graph of the surface.

Accepted Answer

hyperbolic

Question 13

Match the vector-valued function with its graph.

Accepted Answer

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

Question 14

Use graphing technology to sketch the curve traced out by the given vector-valued function.   Use the viewpoint   and   (see figure below).

Accepted Answer

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

Question 15

Find the centripetal force on an object of mass 13 kg with the given position function (in units of meters and seconds).

Accepted Answer

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

Question 16

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 17

A golfer rotates a club with constant angular acceleration   through an angle of   radians. If the angular velocity increases from 0 to 6 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 18

Find the force acting on an object of mass 18 kg with the given position function (in meters and seconds).

Accepted Answer

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

Question 19

Find the derivative of the given vector-valued function.

Accepted Answer

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

Question 20

Find the position function from the given velocity function.

Accepted Answer

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

Label the statement as true (i.e., always true) or false and explain your answer. [Assume that T, N, and B are defined.]

Find the curvature at the given point.

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

Use the graph of below to predict whether the curvature would be larger at or .

Match the vector-valued function with its graph.

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

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

Identify and sketch a graph of the surface.

Which of the following is an arc length parameterization of the given two-dimensional curve? The line segment from to

Use a CAS to estimate the arc length of the curve.

Find the osculating circle at the given point.

Identify and sketch a graph of the surface.

Match the vector-valued function with its graph.

Use graphing technology to sketch the curve traced out by the given vector-valued function. Use the viewpoint and (see figure below).

Find the centripetal force on an object of mass 13 kg with the given position function (in units of meters and seconds).

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

A golfer rotates a club with constant angular acceleration through an angle of radians. If the angular velocity increases from 0 to 6 rad/sec, find .

Find the force acting on an object of mass 18 kg with the given position function (in meters and seconds).

Find the derivative of the given vector-valued function.

Find the position function from the given velocity function.

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

Label the statement as true (i.e., always true) or false and explain your answer. [Assume that T, N, and B are defined.]

Find the curvature at the given point.

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

Use the graph of below to predict whether the curvature would be larger at or .

Match the vector-valued function with its graph.

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

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

Identify and sketch a graph of the surface.

Which of the following is an arc length parameterization of the given two-dimensional curve? The line segment from to

Use a CAS to estimate the arc length of the curve.

Find the osculating circle at the given point.

Identify and sketch a graph of the surface.

Match the vector-valued function with its graph.

Use graphing technology to sketch the curve traced out by the given vector-valued function. Use the viewpoint and (see figure below).

Find the centripetal force on an object of mass 13 kg with the given position function (in units of meters and seconds).

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

A golfer rotates a club with constant angular acceleration through an angle of radians. If the angular velocity increases from 0 to 6 rad/sec, find .

Find the force acting on an object of mass 18 kg with the given position function (in meters and seconds).

Find the derivative of the given vector-valued function.

Find the position function from the given velocity function.

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