Question 1

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

Accepted Answer

A)  horizontal tangents:   , vertical tangents:   
B)  horizontal tangents:   , vertical tangents:   
C)  horizontal tangent:   , vertical tangent:   
D)  horizontal tangents:   , vertical tangents:   
E)  horizontal tangent:   , vertical tangent:   
A)  horizontal tangents:   , vertical tangents:   
B)  horizontal tangents:   , vertical tangents:   
C)  horizontal tangent:   , vertical tangent:   
D)  horizontal tangents:   , vertical tangents:   
E)  horizontal tangent:   , vertical tangent:

Question 2

Find the eccentricity of the polar equation   .

Accepted Answer

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

Question 3

For the given point in rectangular coordinates, find two sets of polar coordinates for the point for   . ​   ​

Accepted Answer

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

Question 4

Find the vertex of the parabola given by   .

Accepted Answer

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

Question 5

Find the length of the curve over the given interval.

Accepted Answer

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

Question 6

Sketch the curve represented by the parametric equations   .

Accepted Answer

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

Question 7

Identify the graph for the polar equation   . ​

Accepted Answer

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

Question 8

Find the area of the region lying between the loops of   .

Accepted Answer

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

Question 9

Find the area of the common interior of the polar equations   and   by sketching the graph of the equations using the graphing utility.

Accepted Answer

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

Question 10

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 11

Find the area of the surface formed by revolving about the   axis the following curve over the given interval. ​   ​

Accepted Answer

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

Question 12

Find a polar equation for the hyperbola with its focus at the pole and vertices   . ​

Accepted Answer

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

Question 13

Find   .

Accepted Answer

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

Question 14

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 15

Find the distance from the pole to the directrix for the conic   . ​

Accepted Answer

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

Question 16

Find an equation of the tangent line at a point   on the curve   .

Accepted Answer

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

Question 17

Match the equation with its graph.

Accepted Answer

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

Question 18

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

Question 19

Convert the polar equation to rectangular form.

Accepted Answer

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

Question 20

Find the area of the inner loop of   .

Accepted Answer

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

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

Find the eccentricity of the polar equation .

For the given point in rectangular coordinates, find two sets of polar coordinates for the point for .

Find the vertex of the parabola given by .

Find the length of the curve over the given interval.

Sketch the curve represented by the parametric equations .

Identify the graph for the polar equation .

Find the area of the region lying between the loops of .

Find the area of the common interior of the polar equations and by sketching the graph of the equations using the graphing utility.

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

Find the area of the surface formed by revolving about the axis the following curve over the given interval.

Find a polar equation for the hyperbola with its focus at the pole and vertices .

Find .

Match the equation with its graph.

Find the distance from the pole to the directrix for the conic .

Find an equation of the tangent line at a point on the curve .

Match the equation with its graph.

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

Convert the polar equation to rectangular form.

Find the area of the inner loop of .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 10: Conics, Parametric Equations, and Polar Coordinates

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

Find the eccentricity of the polar equation .

For the given point in rectangular coordinates, find two sets of polar coordinates for the point for . ​ ​

Find the vertex of the parabola given by .

Find the length of the curve over the given interval.

Sketch the curve represented by the parametric equations .

Identify the graph for the polar equation . ​

Find the area of the region lying between the loops of .

Find the area of the common interior of the polar equations and by sketching the graph of the equations using the graphing utility.

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

Find the area of the surface formed by revolving about the axis the following curve over the given interval. ​ ​

Find a polar equation for the hyperbola with its focus at the pole and vertices . ​

Find .

Match the equation with its graph.

Find the distance from the pole to the directrix for the conic . ​

Find an equation of the tangent line at a point on the curve .

Match the equation with its graph.

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

Convert the polar equation to rectangular form.

Find the area of the inner loop of .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

For the given point in rectangular coordinates, find two sets of polar coordinates for the point for .

Identify the graph for the polar equation .

Find the area of the surface formed by revolving about the axis the following curve over the given interval.

Find a polar equation for the hyperbola with its focus at the pole and vertices .

Find the distance from the pole to the directrix for the conic .

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