Question 1

Find a set of parametric equations for the rectangular equation   .

Accepted Answer

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

Question 2

Use the result, "the set of parametric equations for the ellipse is   " to find a set of parametric equations for the ellipse with vertices   and   and with foci at   and   .

Accepted Answer

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

Question 3

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)    B

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

Question 5

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 6

Identify any points at which the cycloid   is not smooth.

Accepted Answer

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

Question 7

Find a set of parametric equations for the rectangular equation   that satisfies the condition   at the point   .

Accepted Answer

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

Question 8

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle   with the horizontal and having an initial velocity of   feet per second is given by   and   . The center field fence in a ballpark is   feet high and   feet from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of   degrees with the horizontal at a speed of 100 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations   and   . Round your answer to one decimal place.

Accepted Answer

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

Question 9

Find a set of parametric equations for the rectangular equation   that satisfies the condition   at the point   .

Accepted Answer

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

Question 10

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 11

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle   with the horizontal and having an initial velocity of   feet per second is given by   and   . The center field fence in a ballpark is   feet high and   feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of   degrees with the horizontal at a speed of 100 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball.

Accepted Answer

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

Question 12

Use the result, "the set of parametric equations for the circle is   " to find a set of parametric equations for the circle with a center   and radius   .

Accepted Answer

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

Question 13

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 14

Sketch the curve represented by the parametric equations   .

Accepted Answer

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

Question 15

Use the result, "the set of parametric equations for the line passing through   and   is   " to find a set of parametric equations for the line passing through   and   .

Accepted Answer

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

Question 16

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 17

Sketch the curve represented by the parametric equations   .

Accepted Answer

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

Exam 10: Section 2: Conics, Parametric Equations, and Polar Coordinates

Find a set of parametric equations for the rectangular equation .

Use the result, "the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .

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

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

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

Identify any points at which the cycloid is not smooth.

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .

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

Use the result, "the set of parametric equations for the circle is " to find a set of parametric equations for the circle with a center and radius .

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

Sketch the curve represented by the parametric equations .

Use the result, "the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

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

Sketch the curve represented by the parametric equations .

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series

Section 5: Infinite Series

Section 6: Infinite Series

Section 7: Infinite Series

Section 8: Infinite Series