Question 1

At what point on the curve   is the normal plane parallel to the plane   ?

Accepted Answer

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

Question 2

Find the domain of the vector function   .

Accepted Answer

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

Question 3

Let   . Find the domain of   .

Accepted Answer

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

Question 4

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 5

Find the following limit.

Accepted Answer

The answer of Find the following limit.  ...

Question 6

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of   
a.Find the range of the projectile.
b.What is the maximm height attained by the projectile?
c.What is the speed of the projectile at impact?
Round your answers to the nearest integer.

Accepted Answer

a. 32,747

Question 7

If   , find   .

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Find an expression for   .

Accepted Answer

The answer of Find an expression for   ....

Question 10

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 11

Two points A and B are located 100 ft apart on a straight line. A particle moves from A toward B with an initial velocity of 9 ft/sec and an acceleration of     . Simultaneously, a particle moves from B toward A with an initial velocity of 2 ft/sec and an acceleration of     . When will the two particles collide? At what distance from A will the collision take place?

Accepted Answer

The answer of Two points A and B are located...

Question 12

Reparametrize the curve with respect to arc length measured from the point where   in the direction of increasing   .

Accepted Answer

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

Question 13

Find the unit tangent and unit normal vectors   and   for the curve C defined by

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find equations of the normal plane to   at the point (2, 4, 8).

Accepted Answer

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

Question 16

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 17

Find the velocity and position vectors of an object with acceleration   initial velocity   and initial position

Accepted Answer

The answer of Find the velocity and position vectors of...

Question 18

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations   , from   to   . Round your answer to four decimal places.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Given   
a.Find   and   . 
b.Sketch the curve defined by r and the vectors   and   on the same set of axes.

Accepted Answer

The answer of Given   
a.Find   and...

At what point on the curve is the normal plane parallel to the plane ?

Find the domain of the vector function .

Let . Find the domain of .

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

Find the following limit.

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of a.Find the range of the projectile. b.What is the maximm height attained by the projectile? c.What is the speed of the projectile at impact? Round your answers to the nearest integer.

If , find .

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

Find an expression for .

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.

Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

Find the unit tangent and unit normal vectors and for the curve C defined by

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

Find equations of the normal plane to at the point (2, 4, 8).

The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point .

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations , from to . Round your answer to four decimal places.

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

Given a.Find and . b.Sketch the curve defined by r and the vectors and on the same set of axes.

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

At what point on the curve is the normal plane parallel to the plane ?

Find the domain of the vector function .

Let . Find the domain of .

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

Find the following limit.

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of a.Find the range of the projectile. b.What is the maximm height attained by the projectile? c.What is the speed of the projectile at impact? Round your answers to the nearest integer.

If , find .

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

Find an expression for .

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.

Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

Find the unit tangent and unit normal vectors and for the curve C defined by

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

Find equations of the normal plane to at the point (2, 4, 8).

The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point .

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations , from to . Round your answer to four decimal places.

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

Given a.Find and . b.Sketch the curve defined by r and the vectors and on the same set of axes.

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