Question 1

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 2

Plot the given polar point.

Accepted Answer

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

Question 3

Find an equation for the conic section with the given properties. All points such that the difference of the distances to the points
(1, -1) and (1, -11) equals 6

Accepted Answer

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

Question 4

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 5

Find a polar equation corresponding to the given rectangular equation.

Accepted Answer

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

Question 6

Pluto follows an elliptical orbit with a = 20.232 Au (astronomical units) and b = 19.618 Au. Compute the distance the comet travels in one orbit.

Accepted Answer

A)  98.9 Au 
B)  251.2 Au 
C)  128.9 Au 
D)  125.2 Au 
A)  98.9 Au 
B)  251.2 Au 
C)  128.9 Au 
D)  125.2 Au

Question 7

Plot the given polar point.

Accepted Answer

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

Question 8

Find rectangular coordinates for the given polar point.

Accepted Answer

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

Question 9

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 10

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 11

Find the area of the indicated region. Bounded by

Accepted Answer

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

Question 12

Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix

Accepted Answer

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

Question 13

A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 5y2, where should the microphone be placed?

Accepted Answer

A)    units to the right of the focus of the reflector 
B)    units to the right of the vertex of the reflector 
C)  20 units to the right of the focus of the reflector 
D)  10 units to the right of the vertex of the reflector 
A)    units to the right of the focus of the reflector 
B)    units to the right of the vertex of the reflector 
C)  20 units to the right of the focus of the reflector 
D)  10 units to the right of the vertex of the reflector

Question 14

Find the area enclosed by the given curve.

Accepted Answer

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

Question 15

Find an equation for the conic section with the given properties. All points equidistant from the point (-6, -2) and the line y = -4

Accepted Answer

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

Question 16

Starting with the parametric arc length formula   and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve   on the interval [a, b] is given by

Accepted Answer

Let the pa

Question 17

Find the slope of the tangent line to the polar curve at the given point.

Accepted Answer

A)  0 
B)  1 
C)    
D)  undefined 
A)  0 
B)  1 
C)    
D)  undefined

Question 18

Identify all points at which the curve has a vertical tangent.

Accepted Answer

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

Question 19

Find the area enclosed by the given curve.

Accepted Answer

A)    
B)  0 
C)    
D)    
A)    
B)  0 
C)    
D)

Question 20

Find the area enclosed by the given curve.

Accepted Answer

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

Find the rectangular representation of the given polar point.

Plot the given polar point.

Find an equation for the conic section with the given properties. All points such that the difference of the distances to the points (1, -1) and (1, -11) equals 6

Find all polar coordinate representations of the given rectangular point.

Find a polar equation corresponding to the given rectangular equation.

Pluto follows an elliptical orbit with a = 20.232 Au (astronomical units) and b = 19.618 Au. Compute the distance the comet travels in one orbit.

Plot the given polar point.

Find rectangular coordinates for the given polar point.

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

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

Find the area of the indicated region. Bounded by

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 5y², where should the microphone be placed?

Find the area enclosed by the given curve.

Find an equation for the conic section with the given properties. All points equidistant from the point (-6, -2) and the line y = -4

Starting with the parametric arc length formula and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve on the interval [a, b] is given by

Find the slope of the tangent line to the polar curve at the given point.

Identify all points at which the curve has a vertical tangent.

Find the area enclosed by the given curve.

Find the area enclosed by the given curve.

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

Exam 11: Parametric Equations and Polar Coordinates

Find the rectangular representation of the given polar point.

Plot the given polar point.

Find an equation for the conic section with the given properties. All points such that the difference of the distances to the points (1, -1) and (1, -11) equals 6

Find all polar coordinate representations of the given rectangular point.

Find a polar equation corresponding to the given rectangular equation.

Pluto follows an elliptical orbit with a = 20.232 Au (astronomical units) and b = 19.618 Au. Compute the distance the comet travels in one orbit.

Plot the given polar point.

Find rectangular coordinates for the given polar point.

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

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

Find the area of the indicated region. Bounded by

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 5y2, where should the microphone be placed?

Find the area enclosed by the given curve.

Find an equation for the conic section with the given properties. All points equidistant from the point (-6, -2) and the line y = -4

Starting with the parametric arc length formula and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve on the interval [a, b] is given by

Find the slope of the tangent line to the polar curve at the given point.

Identify all points at which the curve has a vertical tangent.

Find the area enclosed by the given curve.

Find the area enclosed by the given curve.

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

A parabolic reflector is used by a sports broadcast engineer to amplify the conversations between football players on the field. If the reflector has the shape x = 5y², where should the microphone be placed?