Question 1

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

Accepted Answer

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Question 2

Match the equation with its graph.

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Question 3

Find an equation of the parabola with vertex   and directrix   .

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Question 4

The path of a projectile is modeled by the parametric equations   and   where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.

Accepted Answer

A)  335.33 ft 
B)  558.88 ft 
C)  73.76 ft 
D)  419.16 ft 
E)  209.58 ft 
A)  335.33 ft 
B)  558.88 ft 
C)  73.76 ft 
D)  419.16 ft 
E)  209.58 ft

Question 5

Match the graph with its polar equation. ​   ​

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Question 6

Convert the polar equation to rectangular form.

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Question 7

Find the length of the curve   over the interval   .

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Question 8

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

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Question 9

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

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Question 10

Convert the rectangular equation to polar form.

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Question 11

Sketch the curve represented by the parametric equations   . ​

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Question 12

Find the second derivative   of the parametric equations   . Round your answer to two decimal places, if necessary.

Accepted Answer

A)  0 
B)  0.88 
C)    
D)  1.14 
E)    
A)  0 
B)  0.88 
C)    
D)  1.14 
E)

Question 13

Find the area of the surface generated by revolving the curve   about the y-axis on the interval   . Round your answer to two decimal places. ​

Accepted Answer

A)  1436.54 
B)  1413.69 
C)  1401.46 
D)  706.85 
E)  2132.77 
A)  1436.54 
B)  1413.69 
C)  1401.46 
D)  706.85 
E)  2132.77

Question 14

Convert the rectangular equation to polar form. x = 2

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Question 15

Find a set of parametric equations for the rectangular equation   .

Accepted Answer

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Question 16

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 17

Find a polar equation for the parabola with its focus at the pole and vertex   .

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Question 18

Find the center of the ellipse given by   .

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Question 19

Find two sets of polar coordinates for the point   for   .

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Question 20

Find the area of the interior of   .

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

Match the equation with its graph.

Find an equation of the parabola with vertex and directrix .

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.

Match the graph with its polar equation.

Convert the polar equation to rectangular form.

Find the length of the curve over the interval .

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

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

Convert the rectangular equation to polar form.

Sketch the curve represented by the parametric equations .

Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.

Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places.

Convert the rectangular equation to polar form. x = 2

Find a set of parametric equations for the rectangular equation .

Identify any points at which the cycloid is not smooth.

Find a polar equation for the parabola with its focus at the pole and vertex .

Find the center of the ellipse given by .

Find two sets of polar coordinates for the point for .

Find the area of the interior 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

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

Match the equation with its graph.

Find an equation of the parabola with vertex and directrix .

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.

Match the graph with its polar equation. ​ ​

Convert the polar equation to rectangular form.

Find the length of the curve over the interval .

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

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

Convert the rectangular equation to polar form.

Sketch the curve represented by the parametric equations . ​

Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.

Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places. ​

Convert the rectangular equation to polar form. x = 2

Find a set of parametric equations for the rectangular equation .

Identify any points at which the cycloid is not smooth.

Find a polar equation for the parabola with its focus at the pole and vertex .

Find the center of the ellipse given by .

Find two sets of polar coordinates for the point for .

Find the area of the interior 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

Match the graph with its polar equation.

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

Sketch the curve represented by the parametric equations .

Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places.