Question 1

Find the length of the curve.   ,   ,

Accepted Answer

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

Question 2

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

Accepted Answer

The answer of Find a Cartesian equation for the curve...

Question 3

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)    C

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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 7

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 8

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...

Question 9

Sketch the polar curve with the given equation.

Accepted Answer

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

Question 10

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 11

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

Accepted Answer

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

Question 12

Find the area enclosed by the curve   .

Accepted Answer

The answer of Find the area enclosed by the curve...

Question 13

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 14

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: @#IMG-DLM& ,

Question 15

The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity   and one focus at the Sun. The length of its major axis is   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   and the aphelion distance is   .) 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

Question 16

Find the Cartesian coordinates of the point   .

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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 19

Find the length of the polar curve.

Accepted Answer

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

Question 20

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)

Find the length of the curve. , ,

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

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

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

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

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

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.

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

Sketch the polar curve with the given equation.

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

Find the area enclosed by the curve .

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

Find the Cartesian coordinates of the point .

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

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

Find the length of the polar curve.

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

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 9: Parametric Equations and Polar Coordinates

Find the length of the curve. , ,

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

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

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

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

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

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.

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

Sketch the polar curve with the given equation.

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

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

Find the area enclosed by the curve .

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

Find the Cartesian coordinates of the point .

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

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

Find the length of the polar curve.

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

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters