Question 1

Find the area of the indicated region. Round to the nearest ten-thousandth. Inner loop of

Accepted Answer

A)  0.3398 
B)  1.5000 
C)  0.2130 
D)  2.7870 
A)  0.3398 
B)  1.5000 
C)  0.2130 
D)  2.7870 A

Question 2

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 3

Find the speed of the object each time it crosses the x-axis. Show all your work.

Accepted Answer

The object crosses the x-axis when y = 0:
y = 8sin t - 5sin 2t = 8sin t - 10sin t cos t = (sin t)(8 - 10cos t) = 0     At t = 0, speed = 2
At   , speed = 18
At   , speed = 14.843
At   , speed = 14.843

Question 4

Find a corresponding x-y equation.

Accepted Answer

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

Question 5

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 6

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Accepted Answer

A)  563.25 
B)  156.87 
C)  840.14 
D)  76.91 
A)  563.25 
B)  156.87 
C)  840.14 
D)  76.91

Question 7

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 8

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 9

Identify all values of   where r = 0.

Accepted Answer

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

Question 10

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 11

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Accepted Answer

A)    
B)  17   
C)    
D)    
A)    
B)  17   
C)    
D)

Question 12

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 13

Find the arc length of the curve exactly.

Accepted Answer

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

Question 14

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Accepted Answer

A)  (0, 0), (0.2338, 0.2025), (1.7457, 1.5118) 
B)  (0, 0) 
C)  (0.2338, -0.2025), (1.7457, -1.5118) 
D)  (0, 0), (0, 1), (0, -1) 
A)  (0, 0), (0.2338, 0.2025), (1.7457, 1.5118) 
B)  (0, 0) 
C)  (0.2338, -0.2025), (1.7457, -1.5118) 
D)  (0, 0), (0, 1), (0, -1)

Question 15

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 16

Find the arc length of the curve exactly.

Accepted Answer

The answer of Find the arc length of the curve...

Question 17

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-5, 5] by [-5, 5]. Directrix y = 2, e = 2

Accepted Answer

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

Question 18

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

Accepted Answer

A)  horizontal component of velocity: 50 vertical component of velocity: -50
Speed:   
B)  horizontal component of velocity: -50 vertical component of velocity: 78
Speed:   
C)  horizontal component of velocity: -50 vertical component of velocity: -78
Speed:   
D)  horizontal component of velocity: 50 vertical component of velocity: 50
Speed:   
A)  horizontal component of velocity: 50 vertical component of velocity: -50
Speed:   
B)  horizontal component of velocity: -50 vertical component of velocity: 78
Speed:   
C)  horizontal component of velocity: -50 vertical component of velocity: -78
Speed:   
D)  horizontal component of velocity: 50 vertical component of velocity: 50
Speed:

Question 19

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 20

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Accepted Answer

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

Find the area of the indicated region. Round to the nearest ten-thousandth. Inner loop of

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find the speed of the object each time it crosses the x-axis. Show all your work.

Find a corresponding x-y equation.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Find all polar coordinate representations of the given rectangular point.

Find the rectangular representation of the given polar point.

Identify all values of where r = 0.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Find the rectangular representation of the given polar point.

Find the arc length of the curve exactly.

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find the arc length of the curve exactly.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-5, 5] by [-5, 5]. Directrix y = 2, e = 2

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

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Exam 11: Parametric Equations and Polar Coordinates

Find the area of the indicated region. Round to the nearest ten-thousandth. Inner loop of

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find the speed of the object each time it crosses the x-axis. Show all your work.

Find a corresponding x-y equation.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Find all polar coordinate representations of the given rectangular point.

Find the rectangular representation of the given polar point.

Identify all values of where r = 0.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Find the rectangular representation of the given polar point.

Find the arc length of the curve exactly.

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Find the arc length of the curve exactly.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-5, 5] by [-5, 5]. Directrix y = 2, e = 2

Parametric equations for the position of an object are given. Find the object's velocity and speed at the given time.

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.) r = 2

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters