Question 1

The helix   intersects the curve   at the point   . Find the angle of intersection.

Accepted Answer

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

Question 2

Find   if   and   .

Accepted Answer

The answer of Find   if   and...

Question 3

Find the limit   .

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

Question 4

Find the domain of the vector function   .

Accepted Answer

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

Question 5

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 6

The torsion of a curve defined by   is given by   Find the torsion of the curve defined by   .

Accepted Answer

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

Question 7

A particle moves with position function   . Find the acceleration of the particle.

Accepted Answer

The answer of A particle moves with position function ...

Question 8

Find the limit   .

Accepted Answer

The answer of Find the limit   ....

Question 9

Find the curvature of   .

Accepted Answer

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

Question 10

Find the length of the curve

Accepted Answer

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

Question 11

Find   if   and   .

Accepted Answer

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

The figure shows a curve   given by a vector function   . Choose the correct expression for   .

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

A force with magnitude   N acts directly upward from the xy-plane on an object with mass   kg. The object starts at the origin with initial velocity   . Find its position function.

Accepted Answer

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

Question 16

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Accepted Answer

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

Question 17

Find the velocity, acceleration, and speed of an object with position function   for   Sketch the path of the object and its velocity and acceleration vectors.

Accepted Answer

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

Question 18

Find the curvature of the curve   .

Accepted Answer

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

Question 19

Find the scalar tangential and normal components of acceleration of a particle with position vector

Accepted Answer

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

Question 20

Find   and   for

Accepted Answer

The answer of Find   and   for...

The helix intersects the curve at the point . Find the angle of intersection.

Find if and .

Find the limit .

Find the domain of the vector function .

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

The torsion of a curve defined by is given by Find the torsion of the curve defined by .

A particle moves with position function . Find the acceleration of the particle.

Find the limit .

Find the curvature of .

Find the length of the curve

Find if and .

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

The figure shows a curve given by a vector function . Choose the correct expression for .

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

A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function.

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Find the curvature of the curve .

Find the scalar tangential and normal components of acceleration of a particle with position vector

Find and for

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

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Exam 13: Vector Functions

The helix intersects the curve at the point . Find the angle of intersection.

Find if and .

Find the limit .

Find the domain of the vector function .

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

The torsion of a curve defined by is given by Find the torsion of the curve defined by .

A particle moves with position function . Find the acceleration of the particle.

Find the limit .

Find the curvature of .

Find the length of the curve

Find if and .

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

The figure shows a curve given by a vector function . Choose the correct expression for .

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

A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function.

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Find the curvature of the curve .

Find the scalar tangential and normal components of acceleration of a particle with position vector

Find and for

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