Question 1

Find the vertices, foci, and directrices of the given ellipse.

Accepted Answer

A)  vertices   ; foci (0, -3), (-14, -3); directrices   
B)  vertices   ; foci (0, -3), (-14, -3); directrices   
C)  vertices (0, -3), (-14, -3); foci   ; directrices   
D)  vertices (0, -3), (-14, -3); foci   ; directrices   
A)  vertices   ; foci (0, -3), (-14, -3); directrices   
B)  vertices   ; foci (0, -3), (-14, -3); directrices   
C)  vertices (0, -3), (-14, -3); foci   ; directrices   
D)  vertices (0, -3), (-14, -3); foci   ; directrices   C

Question 2

Find the area of the indicated region. Bounded by

Accepted Answer

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

Question 3

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

Question 4

Find an equation for the indicated conic section. Ellipse with foci (4, 1), (-8, 1) and vertices (8, 1), (-12, 1)

Accepted Answer

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

Question 5

Find the arc length of the curve. Approximate numerically, if needed.

Accepted Answer

A)  28.274 
B)  14.181 
C)  28.362 
D)  14.137 
A)  28.274 
B)  14.181 
C)  28.362 
D)  14.137

Question 6

The tires on an automobile have a radius of 0.34 meters. If the tires make 12 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

Accepted Answer

A)  92.3 kph 
B)  46.1 kph 
C)  14.7 kph 
D)  29.4 kph 
A)  92.3 kph 
B)  46.1 kph 
C)  14.7 kph 
D)  29.4 kph

Question 7

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: 0
Vertical component of velocity: 7
Speed: 7 
B)  horizontal component of velocity: -3
Vertical component of velocity: 0
Speed: 3 
C)  horizontal component of velocity: 3
Vertical component of velocity: 0
Speed: -3 
D)  horizontal component of velocity:  
Vertical component of velocity:  
Speed:   
A)  horizontal component of velocity: 0
Vertical component of velocity: 7
Speed: 7 
B)  horizontal component of velocity: -3
Vertical component of velocity: 0
Speed: 3 
C)  horizontal component of velocity: 3
Vertical component of velocity: 0
Speed: -3 
D)  horizontal component of velocity:  
Vertical component of velocity:  
Speed:

Question 8

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

Question 9

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

Accepted Answer

A)  -1 
B)    
C)  undefined 
D)  -5 
A)  -1 
B)    
C)  undefined 
D)  -5

Question 10

Find the arc length of the given curve. Round to the nearest ten-thousandth.

Accepted Answer

A)  29.4880 
B)  14.7440 
C)  19.3769 
D)  9.6884 
A)  29.4880 
B)  14.7440 
C)  19.3769 
D)  9.6884

Question 11

Find rectangular coordinates for the given polar point.

Accepted Answer

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

Question 12

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 13

Identify all values of   where r = 0.

Accepted Answer

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

Question 14

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 15

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-1, 1] by [-1, 1]. Directrix y = 1, e = 0.3

Accepted Answer

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

Question 16

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 4 and

Accepted Answer

A)  6.8827 
B)  44.0927 
C)  18.5485 
D)  3.4413 
A)  6.8827 
B)  44.0927 
C)  18.5485 
D)  3.4413

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

Find all points at which |r| is a maximum.

Accepted Answer

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

Question 19

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 20

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

Accepted Answer

A)    
B)    
C)  (1, 1), (1,-1) 
D)  no points of intersection 
A)    
B)    
C)  (1, 1), (1,-1) 
D)  no points of intersection

Find the vertices, foci, and directrices of the given ellipse.

Find the area of the indicated region. Bounded by

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 an equation for the indicated conic section. Ellipse with foci (4, 1), (-8, 1) and vertices (8, 1), (-12, 1)

Find the arc length of the curve. Approximate numerically, if needed.

The tires on an automobile have a radius of 0.34 meters. If the tires make 12 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

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

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 slope of the tangent line to the given curve at the indicated point.

Find the arc length of the given curve. Round to the nearest ten-thousandth.

Find rectangular coordinates for the given polar point.

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

Identify all values of where r = 0.

Find all polar coordinate representations of the given rectangular point.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-1, 1] by [-1, 1]. Directrix y = 1, e = 0.3

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 4 and

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

Find all points at which |r| is a maximum.

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.

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

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 vertices, foci, and directrices of the given ellipse.

Find the area of the indicated region. Bounded by

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 an equation for the indicated conic section. Ellipse with foci (4, 1), (-8, 1) and vertices (8, 1), (-12, 1)

Find the arc length of the curve. Approximate numerically, if needed.

The tires on an automobile have a radius of 0.34 meters. If the tires make 12 revolutions per second, find the speed of the car in kilometers per hour (kph). Round to the nearest tenth. [1 km = 1000 m and 1 hr = 3600 s]

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

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 slope of the tangent line to the given curve at the indicated point.

Find the arc length of the given curve. Round to the nearest ten-thousandth.

Find rectangular coordinates for the given polar point.

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

Identify all values of where r = 0.

Find all polar coordinate representations of the given rectangular point.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-1, 1] by [-1, 1]. Directrix y = 1, e = 0.3

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 4 and

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

Find all points at which |r| is a maximum.

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.

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

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