Question 1

Select the correct Answer: for each question.
-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

Select the correct Answer: for each question.
-The curvature of the curve given by the vector function   is   Use the formula to find the curvature of   at the point

Accepted Answer

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

Question 3

The following table gives coordinates of a particle moving through space along a smooth curve.   Find the average velocity over the time interval   Select the correct Answer

Accepted Answer

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

Question 4

Select the correct Answer for each question.
-Find the length of the curve

Accepted Answer

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

Question 5

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 6

Find the acceleration of a particle with the following position function.   Select the correct Answer

Accepted Answer

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

Question 7

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

Accepted Answer

The answer of The helix   intersects the curve...

Question 8

A particle moves with position function   Find the tangential component of the acceleration vector.Select the correct Answer

Accepted Answer

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

Question 9

Find the limit   Select the correct Answer

Accepted Answer

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

Question 10

Find the velocity of a particle that has the given acceleration and the given initial velocity.Select the correct Answer

Accepted Answer

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

Question 11

Find equations of the normal plane to

Accepted Answer

The answer of Find equations of the normal plane to...

Question 12

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

Accepted Answer

The answer of Find the acceleration of a particle with...

Question 13

Find the length of the curve   Select the correct Answer

Accepted Answer

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

Question 14

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 15

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

The answer of A ball is thrown at an angle...

Question 16

Find parametric equations for the tangent line to the curve with parametric equations     at the point with   Select the correct Answer

Accepted Answer

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

Question 17

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

Accepted Answer

The answer of Find parametric equations for the tangent line...

Question 18

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 19

Find the curvature of the curve   Select the correct Answer

Accepted Answer

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

Question 20

If   .

Accepted Answer

The answer of If   ....

Select the correct Answer: for each question. -The helix intersects the curve at the point Find the angle of intersection.

Select the correct Answer: for each question. -The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point

The following table gives coordinates of a particle moving through space along a smooth curve. Find the average velocity over the time interval Select the correct Answer

Select the correct Answer for each question. -Find the length of the curve

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

Find the acceleration of a particle with the following position function. Select the correct Answer

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

A particle moves with position function Find the tangential component of the acceleration vector.Select the correct Answer

Find the limit Select the correct Answer

Find the velocity of a particle that has the given acceleration and the given initial velocity.Select the correct Answer

Find equations of the normal plane to

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

Find the length of the curve Select the correct Answer

Find the velocity, acceleration, and speed of an object with position 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 parametric equations for the tangent line to the curve with parametric equations at the point with Select the correct Answer

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

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

Find the curvature of the curve Select the correct Answer

If .

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

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

Filters

Exam 13: Vector Functions

Select the correct Answer: for each question. -The helix intersects the curve at the point Find the angle of intersection.

Select the correct Answer: for each question. -The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point

The following table gives coordinates of a particle moving through space along a smooth curve. Find the average velocity over the time interval Select the correct Answer

Select the correct Answer for each question. -Find the length of the curve

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

Find the acceleration of a particle with the following position function. Select the correct Answer

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

A particle moves with position function Find the tangential component of the acceleration vector.Select the correct Answer

Find the limit Select the correct Answer

Find the velocity of a particle that has the given acceleration and the given initial velocity.Select the correct Answer

Find equations of the normal plane to

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

Find the length of the curve Select the correct Answer

Find the velocity, acceleration, and speed of an object with position 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 parametric equations for the tangent line to the curve with parametric equations at the point with Select the correct Answer

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

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

Find the curvature of the curve Select the correct Answer

If .

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

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

Filters