Question 1

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) none of the above 
A)   
  
B)    ​
  
C)    ​
  
D)    ​
  
E) none of the above

Question 2

Find   . ​   ​

Accepted Answer

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

Question 3

Find the length of the curve over the given interval.

Accepted Answer

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

Question 4

Find the arc length of the curve on the given interval. ​

Accepted Answer

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

Question 5

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​   ​

Accepted Answer

A) parabola 
B) ellipse 
C) circle 
D) hyperbola 
A) parabola 
B) ellipse 
C) circle 
D) hyperbola

Question 6

​The position vector of a particle moving in the xy-plane is   for   .For what value of y does the path of the particle have a horizontal tangent? ​

Accepted Answer

A) ​-300 
B) ​   
C) ​25 
D) ​300 
A) ​-300 
B) ​   
C) ​25 
D) ​300

Question 7

Find   . ​   ​

Accepted Answer

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

Question 8

Find the second derivative   of the parametric equations   ,   . ​

Accepted Answer

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

Question 9

Match the equation with the graph shown in red below. ​   ​

Accepted Answer

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

Question 10

Find   given the following vector function. ​   ​

Accepted Answer

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

Question 11

Use the given acceleration function and initial conditions to find the position at time   . ​   ​

Accepted Answer

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

Question 12

Find the area of the inner loop of   . ​

Accepted Answer

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

Question 13

Match the equation with its graph. ​   ​

Accepted Answer

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

Question 14

A particle moves in the yz-plane along the curve represented by the vector-valued function   .Find the minimum value of   . ​

Accepted Answer

A) 6 
B) 4 
C) 7 
D) 9 
E) 8 
A) 6 
B) 4 
C) 7 
D) 9 
E) 8

Question 15

​A particle moves in the xy​-plane so that its velocity vector for time   is   .Which one of the following statements is true about the particle when   ? ​

Accepted Answer

A) ​The particle is speeding up. 
B) ​​The particle is slowing down. 
C) ​​The particle is at rest. 
D) ​​The speed of the particle is   . 
A) ​The particle is speeding up. 
B) ​​The particle is slowing down. 
C) ​​The particle is at rest. 
D) ​​The speed of the particle is   .

Question 16

Determine the interval on which the vector-valued function   is continuous. ​

Accepted Answer

A) (9,∞) 
B) (5,∞) 
C) [5,∞) 
D) [9,∞) 
E) (-5,∞) 
A) (9,∞) 
B) (5,∞) 
C) [5,∞) 
D) [9,∞) 
E) (-5,∞)

Question 17

Find r' (t)given the following vector function. ​   ​

Accepted Answer

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

Question 18

Find r' (t)given the following vector function. ​   ​

Accepted Answer

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

Question 19

Uranus moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 2,876,769,540 kilometers,and the eccentricity is 0.0444.Find the minimum distance (perihelion)of Uranus from the sun.Round your answer to nearest kilometer. ​

Accepted Answer

A) 3,004,498,108 km 
B) 2,749,040,972 km 
C) 2,819,234,149 km 
D) 7,819,870,365 km 
E) 2,934,304,931 km 
A) 3,004,498,108 km 
B) 2,749,040,972 km 
C) 2,819,234,149 km 
D) 7,819,870,365 km 
E) 2,934,304,931 km

Question 20

​A particle moves in the xy-plane such that its position for time   is given by   and   .What is the slope of the tangent to the path of the particle when   ? ​

Accepted Answer

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

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

Find .

Find the length of the curve over the given interval.

Find the arc length of the curve on the given interval.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent?

Find .

Find the second derivative of the parametric equations , .

Match the equation with the graph shown in red below.

Find given the following vector function.

Use the given acceleration function and initial conditions to find the position at time .

Find the area of the inner loop of .

Match the equation with its graph.

A particle moves in the yz-plane along the curve represented by the vector-valued function .Find the minimum value of .

A particle moves in the xy-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ?

Determine the interval on which the vector-valued function is continuous.

Find r' (t)given the following vector function.

Find r' (t)given the following vector function.

Uranus moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 2,876,769,540 kilometers,and the eccentricity is 0.0444.Find the minimum distance (perihelion)of Uranus from the sun.Round your answer to nearest kilometer.

A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ?

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

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

Find . ​ ​

Find the length of the curve over the given interval.

Find the arc length of the curve on the given interval. ​

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ ​

​The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent? ​

Find . ​ ​

Find the second derivative of the parametric equations , . ​

Match the equation with the graph shown in red below. ​ ​

Find given the following vector function. ​ ​

Use the given acceleration function and initial conditions to find the position at time . ​ ​

Find the area of the inner loop of . ​

Match the equation with its graph. ​ ​

A particle moves in the yz-plane along the curve represented by the vector-valued function .Find the minimum value of . ​

​A particle moves in the xy​-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ? ​

Determine the interval on which the vector-valued function is continuous. ​

Find r' (t)given the following vector function. ​ ​

Find r' (t)given the following vector function. ​ ​

Uranus moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 2,876,769,540 kilometers,and the eccentricity is 0.0444.Find the minimum distance (perihelion)of Uranus from the sun.Round your answer to nearest kilometer. ​

​A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ? ​

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

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

Find .

Find the arc length of the curve on the given interval.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

The position vector of a particle moving in the xy-plane is for .For what value of y does the path of the particle have a horizontal tangent?

Find .

Find the second derivative of the parametric equations , .

Match the equation with the graph shown in red below.

Find given the following vector function.

Use the given acceleration function and initial conditions to find the position at time .

Find the area of the inner loop of .

Match the equation with its graph.

A particle moves in the yz-plane along the curve represented by the vector-valued function .Find the minimum value of .

A particle moves in the xy-plane so that its velocity vector for time is .Which one of the following statements is true about the particle when ?

Determine the interval on which the vector-valued function is continuous.

Find r' (t)given the following vector function.

Find r' (t)given the following vector function.

Uranus moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 2,876,769,540 kilometers,and the eccentricity is 0.0444.Find the minimum distance (perihelion)of Uranus from the sun.Round your answer to nearest kilometer.

A particle moves in the xy-plane such that its position for time is given by and .What is the slope of the tangent to the path of the particle when ?