Question 1

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 2

Identify any points at which the Folium of Descartes   is not smooth.Round your answer to two decimal places,if necessary. ​

Accepted Answer

A) not smooth when   
B) not smooth when   
C) not smooth when   
D) smooth everywhere 
E) not smooth when   
A) not smooth when   
B) not smooth when   
C) not smooth when   
D) smooth everywhere 
E) not smooth when

Question 3

Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer. ​

Accepted Answer

A) 55,856,901 km 
B) 11,718,550 km 
C) 58,136,775 km 
D) 68,715,388 km 
E) 45,278,288 km 
A) 55,856,901 km 
B) 11,718,550 km 
C) 58,136,775 km 
D) 68,715,388 km 
E) 45,278,288 km

Question 4

​The position vector of particle moving in the xy-plane is   .What is the distance traveled by the particle from   to   ? Round your answer to three decimal places. ​

Accepted Answer

A) ​9.870 
B) ​10.354 
C) ​12.335 
D) ​42.912 
A) ​9.870 
B) ​10.354 
C) ​12.335 
D) ​42.912

Question 5

Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of   above the horizontal.Use the model for projectile motion,assuming there is no air resistance.Round your answer to three decimal places. ​

Accepted Answer

A) 15,627.500 feet 
B) 8,137.843 feet 
C) 31,252.187 feet 
D) 31,254.999 feet 
E) 16,268.138 feet 
A) 15,627.500 feet 
B) 8,137.843 feet 
C) 31,252.187 feet 
D) 31,254.999 feet 
E) 16,268.138 feet

Question 6

Find all points (if any)of horizontal and vertical tangency to the curve   ,   . ​

Accepted Answer

A) horizontal tangents:   ,vertical tangent: none 
B) horizontal tangent: none,vertical tangents:   
C) horizontal tangents:   ,vertical tangent: none 
D) horizontal tangent: none,vertical tangents:   
E) horizontal tangent: none,vertical tangent: none 
A) horizontal tangents:   ,vertical tangent: none 
B) horizontal tangent: none,vertical tangents:   
C) horizontal tangents:   ,vertical tangent: none 
D) horizontal tangent: none,vertical tangents:   
E) horizontal tangent: none,vertical tangent: none

Question 7

Match the equation with its graph. ​   ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

​The area enclosed inside the polar curve   is ​

Accepted Answer

A) ​14 
B) ​   
C) ​28 
D) ​   
A) ​14 
B) ​   
C) ​28 
D) ​

Question 10

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

Accepted Answer

A) 4 
B) 3 
C) 7 
D) 8 
E) 5 
A) 4 
B) 3 
C) 7 
D) 8 
E) 5

Question 11

Find the area of inside   and outside   by sketching the graph of the equations using the graphing utility. ​

Accepted Answer

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

Question 12

Find the indefinite integral below. ​   ​
Do not include an arbitrary constant vector.
​

Accepted Answer

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

Question 13

Evaluate the limit given below. ​   ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E) The limit does not exist.​ 
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E) The limit does not exist.​

Question 14

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

Accepted Answer

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

Question 15

Find the unit vector in the direction of u. ​   ​

Accepted Answer

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

Question 16

A polar curve is given by   .The slope of the curve at   is...(round your answer to three decimal places,if necessary) ​

Accepted Answer

A) ​0 
B) ​   
C) ​0.5 
D) ​-0.5 
A) ​0 
B) ​   
C) ​0.5 
D) ​-0.5

Question 17

Find the area of the surface generated by revolving the curve about the given axis.   (i)x-axis; (ii)y-axis

Accepted Answer

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

Question 18

Find the eccentricity of the ellipse given by   . ​

Accepted Answer

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

Question 19

Find the domain of the vector-valued function given below. ​   ​

Accepted Answer

A) [ -∞,4) 
B) [0,4] 
C) [-4,4] 
D) (-∞,∞) 
E) [- 4,∞) 
A) [ -∞,4) 
B) [0,4] 
C) [-4,4] 
D) (-∞,∞) 
E) [- 4,∞)

Question 20

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces
Parameter     ​

Accepted Answer

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

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

Identify any points at which the Folium of Descartes is not smooth.Round your answer to two decimal places,if necessary.

Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer.

The position vector of particle moving in the xy-plane is .What is the distance traveled by the particle from to ? Round your answer to three decimal places.

Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal.Use the model for projectile motion,assuming there is no air resistance.Round your answer to three decimal places.

Find all points (if any)of horizontal and vertical tangency to the curve , .

Match the equation with its graph.

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

The area enclosed inside the polar curve is

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

Find the area of inside and outside by sketching the graph of the equations using the graphing utility.

Find the indefinite integral below. Do not include an arbitrary constant vector.

Evaluate the limit given below.

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

Find the unit vector in the direction of u.

A polar curve is given by .The slope of the curve at is...(round your answer to three decimal places,if necessary)

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis

Find the eccentricity of the ellipse given by .

Find the domain of the vector-valued function given below.

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter

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

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

Identify any points at which the Folium of Descartes is not smooth.Round your answer to two decimal places,if necessary. ​

Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer. ​

​The position vector of particle moving in the xy-plane is .What is the distance traveled by the particle from to ? Round your answer to three decimal places. ​

Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal.Use the model for projectile motion,assuming there is no air resistance.Round your answer to three decimal places. ​

Find all points (if any)of horizontal and vertical tangency to the curve , . ​

Match the equation with its graph. ​ ​

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

​The area enclosed inside the polar curve is ​

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

Find the area of inside and outside by sketching the graph of the equations using the graphing utility. ​

Find the indefinite integral below. ​ ​ Do not include an arbitrary constant vector. ​

Evaluate the limit given below. ​ ​

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

Find the unit vector in the direction of u. ​ ​

A polar curve is given by .The slope of the curve at is...(round your answer to three decimal places,if necessary) ​

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis

Find the eccentricity of the ellipse given by . ​

Find the domain of the vector-valued function given below. ​ ​

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter ​

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

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

Identify any points at which the Folium of Descartes is not smooth.Round your answer to two decimal places,if necessary.

Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer.

The position vector of particle moving in the xy-plane is .What is the distance traveled by the particle from to ? Round your answer to three decimal places.

Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal.Use the model for projectile motion,assuming there is no air resistance.Round your answer to three decimal places.

Find all points (if any)of horizontal and vertical tangency to the curve , .

Match the equation with its graph.

The area enclosed inside the polar curve is

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

Find the area of inside and outside by sketching the graph of the equations using the graphing utility.

Find the indefinite integral below. Do not include an arbitrary constant vector.

Evaluate the limit given below.

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

Find the unit vector in the direction of u.

A polar curve is given by .The slope of the curve at is...(round your answer to three decimal places,if necessary)

Find the eccentricity of the ellipse given by .

Find the domain of the vector-valued function given below.

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter