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

Question 2

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

Question 3

Plot the given polar point.

Accepted Answer

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

Question 4

Find all slopes of the curve at the given point. [It may be helpful to graph the curve.]

Accepted Answer

A)    
B)  -3 and 0 
C)  -3 and 3 
D)  0, undefined 
A)    
B)  -3 and 0 
C)  -3 and 3 
D)  0, undefined

Question 5

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix x = 2, e = 1

Accepted Answer

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

Question 6

Identify a range of values of   that produces one copy of the graph.

Accepted Answer

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

Question 7

Find the arc length of the curve exactly.

Accepted Answer

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

Question 8

Find an x-y equation for the given parametric equations.

Accepted Answer

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

Question 9

For the given parametric equations, find a corresponding x-y equation for the curve.

Accepted Answer

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

Question 10

For the given parametric equations, find a corresponding x-y equation for the curve.

Accepted Answer

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

Question 11

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -2, e = 4

Accepted Answer

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

Question 12

The time required for a skier, initially at rest, to ski from point A to point B on an inclined plane (where B is not directly downhill from
A ) 5.4802k

Accepted Answer

A)  is given by:   . In the equation above, a is the value of the parameter u at point A , b is the value of u at point B , and k is a constant. The expressions x(u ) and y(u ) represent parametrically the trajectory taken by the skier. The "straight downhill" direction is assumed to be in the direction of increasing values of y.
Find the time required to complete the trip if the skier chooses the following trajectory:   . 
B)  5.0956k 
C)  91.310k 
D)  90.2388k 
A)  is given by:   . In the equation above, a is the value of the parameter u at point A , b is the value of u at point B , and k is a constant. The expressions x(u ) and y(u ) represent parametrically the trajectory taken by the skier. The "straight downhill" direction is assumed to be in the direction of increasing values of y.
Find the time required to complete the trip if the skier chooses the following trajectory:   . 
B)  5.0956k 
C)  91.310k 
D)  90.2388k

Question 13

The orbits of the planets can be modeled easily by assuming i). that the sun is a perfect sphere and ii). that each planet is influenced only by the gravitational field of the sun (that is, each planet is unperturbed by gravitational forces from other planets, distant stars, etc.). According to Newton's (classical) theory of gravity, these assumptions result in elliptical planetary orbits with the sun at one focus. That is, the orbit can be described by the polar equation   . However, according to Einstein's (relativistic) theory of gravitation, the orbits are more accurately described by   , where   is a constant such that   . Describe how the inclusion of the factor   affects the orbit. That is, compare the classical orbit to the relativistic orbit. How do they differ? Draw figures that summarize the differences in the classical and relativistic orbits.

Accepted Answer

The period of the relativistic orbit is

Question 14

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: -34
Vertical component of velocity: -17
Speed:   
B)  horizontal component of velocity: 34
Vertical component of velocity: 47
Speed:   
C)  horizontal component of velocity: 34
Vertical component of velocity: -47
Speed:   
D)  horizontal component of velocity: -34
Vertical component of velocity: 17
Speed:   
A)  horizontal component of velocity: -34
Vertical component of velocity: -17
Speed:   
B)  horizontal component of velocity: 34
Vertical component of velocity: 47
Speed:   
C)  horizontal component of velocity: 34
Vertical component of velocity: -47
Speed:   
D)  horizontal component of velocity: -34
Vertical component of velocity: 17
Speed:

Question 15

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 16

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

Accepted Answer

A)  989.5894 
B)  184.000 
C)  690.6874 
D)  549.4286 
A)  989.5894 
B)  184.000 
C)  690.6874 
D)  549.4286

Question 17

Find the arc length of the curve exactly.

Accepted Answer

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

Question 18

Find all points of intersection of the two curves.

Accepted Answer

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

Question 19

Find parametric equations describing the given curve.
The line segment from   to

Accepted Answer

Answers ma

Question 20

Find a polar equation corresponding to the given rectangular equation.

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

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

Plot the given polar point.

Find all slopes of the curve at the given point. [It may be helpful to graph the curve.]

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix x = 2, e = 1

Identify a range of values of that produces one copy of the graph.

Find the arc length of the curve exactly.

Find an x-y equation for the given parametric equations.

For the given parametric equations, find a corresponding x-y equation for the curve.

For the given parametric equations, find a corresponding x-y equation for the curve.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -2, e = 4

The time required for a skier, initially at rest, to ski from point A to point B on an inclined plane (where B is not directly downhill from A ) 5.4802k

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

Find all polar coordinate representations of the given rectangular point.

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

Find the arc length of the curve exactly.

Find all points of intersection of the two curves.

Find parametric equations describing the given curve. The line segment from to

Find a polar equation corresponding to the given rectangular equation.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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

Exam 10: Parametric Equations and Polar Coordinates

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

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

Plot the given polar point.

Find all slopes of the curve at the given point. [It may be helpful to graph the curve.]

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix x = 2, e = 1

Identify a range of values of that produces one copy of the graph.

Find the arc length of the curve exactly.

Find an x-y equation for the given parametric equations.

For the given parametric equations, find a corresponding x-y equation for the curve.

For the given parametric equations, find a corresponding x-y equation for the curve.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -2, e = 4

The time required for a skier, initially at rest, to ski from point A to point B on an inclined plane (where B is not directly downhill from A ) 5.4802k

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

Find all polar coordinate representations of the given rectangular point.

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

Find the arc length of the curve exactly.

Find all points of intersection of the two curves.

Find parametric equations describing the given curve. The line segment from to

Find a polar equation corresponding to the given rectangular equation.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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