Question 1

Find the acceleration function for the given position function.

Accepted Answer

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Question 2

Evaluate the given integral.

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D)

Question 3

Find the derivative of the given vector-valued function.

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D)

Question 4

Identify and sketch a graph of the surface.

Accepted Answer

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

Question 5

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

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D)    
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D)

Question 6

Find the curvature at the given point.

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Question 7

Find the osculating circle at the given point.

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D)

Question 8

Find parametric equations for the indicated curve.
The intersection of   and z = 2

Accepted Answer

Answers may vary. On

Question 9

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

Accepted Answer

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B)    
C)    
D)    
A)    
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D)

Question 10

Find the position function from the given velocity function.

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D)

Question 11

Identify and sketch a graph of the surface.

Accepted Answer

elliptic p

Question 12

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

Accepted Answer

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

Question 13

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

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B)    
C)    
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D)

Question 14

Find the derivative of the given vector-valued function.

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C)    
D)    
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B)    
C)    
D)

Question 15

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 16

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

Accepted Answer

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C)    
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D)

Question 17

Find the centripetal force on an object of mass 14 kg with the given position function (in units of meters and seconds).

Accepted Answer

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Question 18

Find the force acting on an object of mass 23 kg with the given position function (in meters and seconds).

Accepted Answer

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D)    
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Question 19

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)  216.6 ft 
B)  836.6 ft 
C)  231.4 ft 
D)  1448.8 ft 
A)  216.6 ft 
B)  836.6 ft 
C)  231.4 ft 
D)  1448.8 ft

Question 20

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)  187.7 ft 
B)  530.9 ft 
C)  155.0 ft 
D)  750.8 ft 
A)  187.7 ft 
B)  530.9 ft 
C)  155.0 ft 
D)  750.8 ft

Find the acceleration function for the given position function.

Evaluate the given integral.

Find the derivative of the given vector-valued function.

Identify and sketch a graph of the surface.

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

Find the curvature at the given point.

Find the osculating circle at the given point.

Find parametric equations for the indicated curve. The intersection of and z = 2

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

Find the position function from the given velocity function.

Identify and sketch a graph of the surface.

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

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

Find the derivative of the given vector-valued function.

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

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

Find the centripetal force on an object of mass 14 kg with the given position function (in units of meters and seconds).

Find the force acting on an object of mass 23 kg with the given position function (in meters and seconds).

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.

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.

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

Find the acceleration function for the given position function.

Evaluate the given integral.

Find the derivative of the given vector-valued function.

Identify and sketch a graph of the surface.

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

Find the curvature at the given point.

Find the osculating circle at the given point.

Find parametric equations for the indicated curve. The intersection of and z = 2

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

Find the position function from the given velocity function.

Identify and sketch a graph of the surface.

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

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

Find the derivative of the given vector-valued function.

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

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

Find the centripetal force on an object of mass 14 kg with the given position function (in units of meters and seconds).

Find the force acting on an object of mass 23 kg with the given position function (in meters and seconds).

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.

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.

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