Question 1

Find the acceleration of a particle with the following position function.

Accepted Answer

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B)    
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D)    
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E)

Question 2

Find the limit.

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E)

Question 3

Find the unit tangent and unit normal vectors   and   for the curve C defined by   Sketch the graph of C, and show   and   for

Accepted Answer

The answer of Find the unit tangent and unit normal...

Question 4

Find the derivative

Accepted Answer

The answer of Find the derivative  ...

Question 5

The position function of a particle is given by   When is the speed a minimum?

Accepted Answer

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D)    
E)

Question 6

Find the unit tangent vector   .

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E)

Question 7

Find the curvature of the curve   .

Accepted Answer

A) 0 
B) 11 
C) 1 
D)    
A) 0 
B) 11 
C) 1 
D)

Question 8

Find the unit tangent vector for the curve given by   .

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
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B)    
C)    
D)    
E) None of these

Question 9

Find the integral

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Question 10

Sketch the curve of the vector function     and indicate the orientation of the curve.

Accepted Answer

The answer of Sketch the curve of the vector function...

Question 11

If   , evaluate   .

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E)

Question 12

Find the velocity, acceleration, and speed of an object with position vector   .

Accepted Answer

The answer of Find the velocity, acceleration, and speed of...

Question 13

Find the point of intersection of the tangent lines to the curve   , at the points where   and   .

Accepted Answer

The answer of Find the point of intersection of the...

Question 14

Find the length of the curve

Accepted Answer

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

Question 15

For the curve given by   , find the unit normal vector.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 16

A ball is thrown at an angle of   to the ground. If the ball lands   m away, what was the initial speed of the ball? Let   .

Accepted Answer

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

Question 17

Find the position vector of a particle that has the given acceleration and the given initial velocity and position.

Accepted Answer

The answer of Find the position vector of a particle...

Question 18

Find the point(s) on the graph of   at which the curvature is zero.

Accepted Answer

The answer of Find the point(s) on the graph of...

Question 19

Find the speed of a particle with the given position function.

Accepted Answer

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

Question 20

Find the length of the curve

Accepted Answer

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

Find the acceleration of a particle with the following position function.

Find the limit.

Find the unit tangent and unit normal vectors and for the curve C defined by Sketch the graph of C, and show and for

Find the derivative

The position function of a particle is given by When is the speed a minimum?

Find the unit tangent vector .

Find the curvature of the curve .

Find the unit tangent vector for the curve given by .

Find the integral

Sketch the curve of the vector function and indicate the orientation of the curve.

If , evaluate .

Find the velocity, acceleration, and speed of an object with position vector .

Find the point of intersection of the tangent lines to the curve , at the points where and .

Find the length of the curve

For the curve given by , find the unit normal vector.

A ball is thrown at an angle of to the ground. If the ball lands m away, what was the initial speed of the ball? Let .

Find the position vector of a particle that has the given acceleration and the given initial velocity and position.

Find the point(s) on the graph of at which the curvature is zero.

Find the speed of a particle with the given position function.

Find the length of the curve

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 13: Vector Functions

Find the acceleration of a particle with the following position function.

Find the limit.

Find the unit tangent and unit normal vectors and for the curve C defined by Sketch the graph of C, and show and for

Find the derivative

The position function of a particle is given by When is the speed a minimum?

Find the unit tangent vector .

Find the curvature of the curve .

Find the unit tangent vector for the curve given by .

Find the integral

Sketch the curve of the vector function and indicate the orientation of the curve.

If , evaluate .

Find the velocity, acceleration, and speed of an object with position vector .

Find the point of intersection of the tangent lines to the curve , at the points where and .

Find the length of the curve

For the curve given by , find the unit normal vector.

A ball is thrown at an angle of to the ground. If the ball lands m away, what was the initial speed of the ball? Let .

Find the position vector of a particle that has the given acceleration and the given initial velocity and position.

Find the point(s) on the graph of at which the curvature is zero.

Find the speed of a particle with the given position function.

Find the length of the curve

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters