Question 1

Find the component form of vector u + v given   and   and the angles that u and v make with the positive x-axis are   and   . ​

Accepted Answer

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

Question 2

The position vector   describes the path of an object moving in space.Find the velocity v(t)of the object. ​

Accepted Answer

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

Question 3

Find the arc length of the curve   ,   on the interval   .Round your answer to three decimal places. ​

Accepted Answer

A) 384.650 
B) 256.433 
C) 259.131 
D) 89.195 
E) 133.793 
A) 384.650 
B) 256.433 
C) 259.131 
D) 89.195 
E) 133.793

Question 4

Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​   ​

Accepted Answer

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

Question 5

Find the area of the interior of   . ​

Accepted Answer

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

Question 6

Given   ,find   . ​

Accepted Answer

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

Question 7

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters.The slide has a height of 2 meters and makes one complete revolution from top to bottom.Find a vector-valued function for the helix. ​

Accepted Answer

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

Question 8

Find an equation of the hyperbola with vertices   and asymptotes   . ​

Accepted Answer

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

Question 9

Match the equation with its graph. ​   ​

Accepted Answer

A) ​
  
B) ​ ​
  
C) ​ ​
  
D) ​ ​
  
E) none of these 
A) ​
  
B) ​ ​
  
C) ​ ​
  
D) ​ ​
  
E) none of these

Question 10

Represent the following curve by a vector-valued function. ​   ​

Accepted Answer

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

Question 11

Write the corresponding rectangular equation for the curve represented by the parametric equations   by eliminating the parameter. ​

Accepted Answer

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

Question 12

Find the magnitude of the vector given below.Round your answer to four decimal places. ​   ​

Accepted Answer

A) 0 
B)    
C)    
D)    
E)    
A) 0 
B)    
C)    
D)    
E)

Question 13

Find the vertex,focus,and directrix of the parabola and sketch its graph. ​   ​

Accepted Answer

A) vertex:   ;focus:
  ;directrix
 
​
  
B) vertex:   ;focus:
  ;directrix
 
​
  
C) vertex:   ;focus:
  ;directrix
 
​
  
D) vertex:   ;focus:
  ;directrix
 
​
​
  
E) vertex:   ;focus:
  ;directrix
 
​
  
A) vertex:   ;focus:
  ;directrix
 
​
  
B) vertex:   ;focus:
  ;directrix
 
​
  
C) vertex:   ;focus:
  ;directrix
 
​
  
D) vertex:   ;focus:
  ;directrix
 
​
​
  
E) vertex:   ;focus:
  ;directrix
 
​

Question 14

Given   and   ,find   . ​

Accepted Answer

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

Question 15

Find the length of the curve over the given interval. ​   ​

Accepted Answer

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

Question 16

Use the properties of the derivative to find   given the following vector-valued functions. ​   ​

Accepted Answer

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

Question 17

The position vector   describes the path of an object moving in space.Find the speed   of the object. ​

Accepted Answer

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

Question 18

The position vector   describes the path of an object moving in space.Find the acceleration   of the object. ​

Accepted Answer

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

Question 19

A baseball,hit 5 feet above the ground,leaves the bat at an angle of   and its caught by an outfielder 5 feet above the ground and 500 feet from home plate.How high does the ball rise? Round your answer to the nearest integer. ​

Accepted Answer

A) 77 feet 
B) 10 feet 
C) 167 feet 
D) 118 feet 
E) 23 feet 
A) 77 feet 
B) 10 feet 
C) 167 feet 
D) 118 feet 
E) 23 feet

Question 20

​The path of a particle in the xy-plane is given by the parametric equations   and   for   .An integral expression that represents the length of the path from   to   is ​

Accepted Answer

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

Find the component form of vector u + v given and and the angles that u and v make with the positive x-axis are and .

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object.

Find the arc length of the curve , on the interval .Round your answer to three decimal places.

Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter.

Find the area of the interior of .

Given ,find .

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters.The slide has a height of 2 meters and makes one complete revolution from top to bottom.Find a vector-valued function for the helix.

Find an equation of the hyperbola with vertices and asymptotes .

Match the equation with its graph.

Represent the following curve by a vector-valued function.

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.

Find the magnitude of the vector given below.Round your answer to four decimal places.

Find the vertex,focus,and directrix of the parabola and sketch its graph.

Given and ,find .

Find the length of the curve over the given interval.

Use the properties of the derivative to find given the following vector-valued functions.

The position vector describes the path of an object moving in space.Find the speed of the object.

The position vector describes the path of an object moving in space.Find the acceleration of the object.

A baseball,hit 5 feet above the ground,leaves the bat at an angle of and its caught by an outfielder 5 feet above the ground and 500 feet from home plate.How high does the ball rise? Round your answer to the nearest integer.

The path of a particle in the xy-plane is given by the parametric equations and for .An integral expression that represents the length of the path from to is

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Find the component form of vector u + v given and and the angles that u and v make with the positive x-axis are and . ​

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object. ​

Find the arc length of the curve , on the interval .Round your answer to three decimal places. ​

Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter. ​ ​

Find the area of the interior of . ​

Given ,find . ​

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters.The slide has a height of 2 meters and makes one complete revolution from top to bottom.Find a vector-valued function for the helix. ​

Find an equation of the hyperbola with vertices and asymptotes . ​

Match the equation with its graph. ​ ​

Represent the following curve by a vector-valued function. ​ ​

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter. ​

Find the magnitude of the vector given below.Round your answer to four decimal places. ​ ​

Find the vertex,focus,and directrix of the parabola and sketch its graph. ​ ​

Given and ,find . ​

Find the length of the curve over the given interval. ​ ​

Use the properties of the derivative to find given the following vector-valued functions. ​ ​

The position vector describes the path of an object moving in space.Find the speed of the object. ​

The position vector describes the path of an object moving in space.Find the acceleration of the object. ​

A baseball,hit 5 feet above the ground,leaves the bat at an angle of and its caught by an outfielder 5 feet above the ground and 500 feet from home plate.How high does the ball rise? Round your answer to the nearest integer. ​

​The path of a particle in the xy-plane is given by the parametric equations and for .An integral expression that represents the length of the path from to is ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the component form of vector u + v given and and the angles that u and v make with the positive x-axis are and .

The position vector describes the path of an object moving in space.Find the velocity v(t)of the object.

Find the arc length of the curve , on the interval .Round your answer to three decimal places.

Sketch the curve represented by the parametric equations,and write the corresponding rectangular equation by eliminating the parameter.

Find the area of the interior of .

Given ,find .

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters.The slide has a height of 2 meters and makes one complete revolution from top to bottom.Find a vector-valued function for the helix.

Find an equation of the hyperbola with vertices and asymptotes .

Match the equation with its graph.

Represent the following curve by a vector-valued function.

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.

Find the magnitude of the vector given below.Round your answer to four decimal places.

Find the vertex,focus,and directrix of the parabola and sketch its graph.

Given and ,find .

Find the length of the curve over the given interval.

Use the properties of the derivative to find given the following vector-valued functions.

The position vector describes the path of an object moving in space.Find the speed of the object.

The position vector describes the path of an object moving in space.Find the acceleration of the object.

A baseball,hit 5 feet above the ground,leaves the bat at an angle of and its caught by an outfielder 5 feet above the ground and 500 feet from home plate.How high does the ball rise? Round your answer to the nearest integer.

The path of a particle in the xy-plane is given by the parametric equations and for .An integral expression that represents the length of the path from to is