Question 1

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 2

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

Accepted Answer

Answers may vary with respect to the loc

Question 3

Find the curvature at the given point.

Accepted Answer

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

Question 4

Evaluate the given integral.

Accepted Answer

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

Question 5

Match the vector-valued function with its graph.

Accepted Answer

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

Question 6

Find the velocity function for the given position function.

Accepted Answer

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

Question 7

Find the position function from the given acceleration function.

Accepted Answer

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

Question 8

Find the tangential and normal components of acceleration for the given position function at the indicated point.

Accepted Answer

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

Question 9

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

Accepted Answer

A)  4.4 
B)  4.3 
C)  3.9 
D)  5.7 
A)  4.4 
B)  4.3 
C)  3.9 
D)  5.7

Question 10

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

Accepted Answer

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

Question 11

Find the acceleration function for the given position function.

Accepted Answer

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

Question 12

Find the magnitude of the net force on an object of mass 11 kg with the given position function (in units of meters and seconds).

Accepted Answer

A)  4235 Newtons 
B)  2695 Newtons 
C)  385 Newtons 
D)  1925 Newtons 
A)  4235 Newtons 
B)  2695 Newtons 
C)  385 Newtons 
D)  1925 Newtons

Question 13

Find the velocity function for the given position function.

Accepted Answer

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

Question 14

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 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 limit if it exists.

Accepted Answer

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

Question 17

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 maximum altitude. Round to the nearest tenth of a foot.

Accepted Answer

A)  760.8 ft 
B)  2133.5 ft 
C)  311.0 ft 
D)  3013.1 ft 
A)  760.8 ft 
B)  2133.5 ft 
C)  311.0 ft 
D)  3013.1 ft

Question 18

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 19

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 20

Identify and sketch a graph of the surface.

Accepted Answer

The answer of Identify and sketch a graph of the...

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

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

Find the curvature at the given point.

Evaluate the given integral.

Match the vector-valued function with its graph.

Find the velocity function for the given position function.

Find the position function from the given acceleration function.

Find the tangential and normal components of acceleration for the given position function at the indicated point.

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

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

Find the acceleration function for the given position function.

Find the magnitude of the net force on an object of mass 11 kg with the given position function (in units of meters and seconds).

Find the velocity function for the given position function.

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

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

Find the limit if it exists.

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 maximum altitude. Round to the nearest tenth of a foot.

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

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

Identify and sketch a graph of the surface.

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

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

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

Find the curvature at the given point.

Evaluate the given integral.

Match the vector-valued function with its graph.

Find the velocity function for the given position function.

Find the position function from the given acceleration function.

Find the tangential and normal components of acceleration for the given position function at the indicated point.

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

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

Find the acceleration function for the given position function.

Find the magnitude of the net force on an object of mass 11 kg with the given position function (in units of meters and seconds).

Find the velocity function for the given position function.

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

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

Find the limit if it exists.

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 maximum altitude. Round to the nearest tenth of a foot.

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

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

Identify and sketch a graph of the surface.

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