Question 1

Find the eccentricity of the conic.

Accepted Answer

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

Question 2

Select the curve by using the parametric equations to plot the points.

Accepted Answer

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

Question 3

The orbit of Hale-Bopp comet,discovered in 1995,is an ellipse with eccentricity 0.995 and one focus at the Sun.The length of its major axis is 369.9 AU.[An astronomical unit (AU)is the mean distance between Earth and the Sun,about 93 million miles.] Find the maximum distance from the comet to the Sun.(The perihelion distance from a planet to the Sun is a(1-e) and the aphelion distance is a(1+e) .Find the answer in AU and round to the nearest hundredth.

Accepted Answer

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

Question 4

Find the area that the curve encloses.

Accepted Answer

The answer of Find the area that the curve encloses....

Question 5

Find a polar equation for the curve represented by the given Cartesian equation.

Accepted Answer

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

Question 6

Consider the polar equation   .
(a)Find the eccentricity and an equation of the directrix of the conic.
(b)Identify the conic.
(c)Sketch the curve.

Accepted Answer

(a)eccentricity: 1 ,

Question 7

Find the Cartesian coordinates of the point   .

Accepted Answer

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

Question 8

Select the curve by using the parametric equations to plot the points.

Accepted Answer

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

Question 9

Write a polar equation in r and $ \theta $ of an ellipse with the focus at the origin,with the eccentricity   and vertex at   .

Accepted Answer

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

Question 10

Write a polar equation in r and   of a hyperbola with the focus at the origin,with the eccentricity   and directrix   .

Accepted Answer

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

Question 11

Find the length of the curve.   ,   ,

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these 
A)    
B)    
C)    
D)    
E)  None of these

Question 12

Find the area of the region that lies inside the first curve and outside the second curve.

Accepted Answer

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

Question 13

The graph of the following curve is given.Find the area that it encloses.

Accepted Answer

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

Question 14

Set up,but do not evaluate,an integral that represents the length of the parametric curve.

Accepted Answer

The answer of Set up,but do not evaluate,an integral that...

Question 15

Write a polar equation in r and $ \theta $of an ellipse with the focus at the origin,with the eccentricity   and directrix   .

Accepted Answer

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

Question 16

Consider the polar equation   .
(a)Find the eccentricity and an equation of the directrix of the conic.
(b)Identify the conic.
(c)Sketch the curve.

Accepted Answer

(a)eccentricity: 2 ,

Question 17

Match the parametric equations with the graphs labeled a-e.

Accepted Answer

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

Question 18

The planet Mercury travels in an elliptical orbit with eccentricity 0.403 .Its minimum distance from the Sun is   km.If the perihelion distance from a planet to the Sun is a (1- e) and the aphelion distance is a (1+e) ,find the maximum distance (in km)from Mercury to the Sun.

Accepted Answer

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

Question 19

Find the area of the region enclosed by one loop of the curve.

Accepted Answer

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

Question 20

Set up an integral that represents the length of the curve.Then use your calculator to find the length correct to four decimal places.

Accepted Answer

The answer of Set up an integral that represents the...

Find the eccentricity of the conic.

Select the curve by using the parametric equations to plot the points.

Find the area that the curve encloses.

Find a polar equation for the curve represented by the given Cartesian equation.

Consider the polar equation . (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

Find the Cartesian coordinates of the point .

Select the curve by using the parametric equations to plot the points.

Write a polar equation in r and of a hyperbola with the focus at the origin,with the eccentricity and directrix .

Find the length of the curve. , ,

Find the area of the region that lies inside the first curve and outside the second curve.

The graph of the following curve is given.Find the area that it encloses.

Set up,but do not evaluate,an integral that represents the length of the parametric curve.

Consider the polar equation . (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

Match the parametric equations with the graphs labeled a-e.

The planet Mercury travels in an elliptical orbit with eccentricity 0.403 .Its minimum distance from the Sun is km.If the perihelion distance from a planet to the Sun is a (1- e) and the aphelion distance is a (1+e) ,find the maximum distance (in km)from Mercury to the Sun.

Find the area of the region enclosed by one loop of the curve.

Set up an integral that represents the length of the curve.Then use your calculator to find the length correct to four decimal places.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

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Ectors and the Geometry of Space

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Vector Calculus

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Exam 9: Parametric Equations and Polar Coordinates

Find the eccentricity of the conic.

Select the curve by using the parametric equations to plot the points.

Find the area that the curve encloses.

Find a polar equation for the curve represented by the given Cartesian equation.

Consider the polar equation . (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

Find the Cartesian coordinates of the point .

Select the curve by using the parametric equations to plot the points.

Write a polar equation in r and θ \theta θ of an ellipse with the focus at the origin,with the eccentricity and vertex at .

Write a polar equation in r and of a hyperbola with the focus at the origin,with the eccentricity and directrix .

Find the length of the curve. , ,

Find the area of the region that lies inside the first curve and outside the second curve.

The graph of the following curve is given.Find the area that it encloses.

Set up,but do not evaluate,an integral that represents the length of the parametric curve.

Write a polar equation in r and θ \theta θ of an ellipse with the focus at the origin,with the eccentricity and directrix .

Consider the polar equation . (a)Find the eccentricity and an equation of the directrix of the conic. (b)Identify the conic. (c)Sketch the curve.

Match the parametric equations with the graphs labeled a-e.

The planet Mercury travels in an elliptical orbit with eccentricity 0.403 .Its minimum distance from the Sun is km.If the perihelion distance from a planet to the Sun is a (1- e) and the aphelion distance is a (1+e) ,find the maximum distance (in km)from Mercury to the Sun.

Find the area of the region enclosed by one loop of the curve.

Set up an integral that represents the length of the curve.Then use your calculator to find the length correct to four decimal places.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters