Question 1

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 2

Graph the conic section with focus   and the given directrix and eccentricity. Directrix

Accepted Answer

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

Question 3

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 y = -1, e = 3

Accepted Answer

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

Question 4

Which graph below corresponds to the given parametric equations?

Accepted Answer

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

Question 5

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 6

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

Accepted Answer

A)  vertices (5, -17), (5, 1); foci   , directrices   
B)  vertices (-4, -8), (14, -8); foci   , directrices   
C)  vertices (5, -17), (5, 1); foci   , directrices   
D)  vertices (-4, -8), (14, -8); foci   , directrices   
A)  vertices (5, -17), (5, 1); foci   , directrices   
B)  vertices (-4, -8), (14, -8); foci   , directrices   
C)  vertices (5, -17), (5, 1); foci   , directrices   
D)  vertices (-4, -8), (14, -8); foci   , directrices

Question 7

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 8

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

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

Question 9

Using the limit definition of integration, show that the area A bounded by the polar curve   and the rays   and   is given by

Accepted Answer

Partition the interval @#IMG-DLM& into n

Question 10

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

Accepted Answer

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

Question 11

Find all points of intersection of the two curves.

Accepted Answer

A)    
B)    
C)    
D)  The curves have no points of intersection. 
A)    
B)    
C)    
D)  The curves have no points of intersection.

Question 12

Find an equation for the indicated conic section. Parabola with focus (-6, 3) and directrix x = 0

Accepted Answer

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

Question 13

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 14

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 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:   .

Accepted Answer

A)  5.4802k 
B)  5.0956k 
C)  91.310k 
D)  90.2388k 
A)  5.4802k 
B)  5.0956k 
C)  91.310k 
D)  90.2388k

Question 15

Find the vertex, focus, and directrix of the given parabola.

Accepted Answer

A)  vertex (-6, 6); focus   ; directrix   
B)  vertex (6, -6); focus   ; directrix   
C)  vertex   ; focus (6, -6); directrix   
D)  vertex (6, -6); focus   ; directrix   
A)  vertex (-6, 6); focus   ; directrix   
B)  vertex (6, -6); focus   ; directrix   
C)  vertex   ; focus (6, -6); directrix   
D)  vertex (6, -6); focus   ; directrix

Question 16

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 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 [-1, 1] by [-1, 1]. Directrix y = 1, e = 0.3

Accepted Answer

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

Question 18

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

Accepted Answer

A)  (0, 0), (0.9428, 0.3333), (-0.9428, 0.3333) 
B)  (0, 0) 
C)  (0, 0), (0.2528, 0.8333), (2.7472, 0.8333) 
D)  (0, 0), (0.2528, -0.8333), (2.7472, -0.8333) 
A)  (0, 0), (0.9428, 0.3333), (-0.9428, 0.3333) 
B)  (0, 0) 
C)  (0, 0), (0.2528, 0.8333), (2.7472, 0.8333) 
D)  (0, 0), (0.2528, -0.8333), (2.7472, -0.8333)

Question 19

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

Accepted Answer

A)    
B)  1 
C)  -1 
D)    
A)    
B)  1 
C)  -1 
D)

Question 20

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

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

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

Graph the conic section with focus and the given directrix and eccentricity. Directrix

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 y = -1, e = 3

Which graph below corresponds to the given parametric equations?

Find the rectangular representation of the given polar point.

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

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

Sketch the plane curve defined by the given parametric equations.

Using the limit definition of integration, show that the area A bounded by the polar curve and the rays and is given by

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

Find all points of intersection of the two curves.

Find an equation for the indicated conic section. Parabola with focus (-6, 3) and directrix x = 0

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 vertex, focus, and directrix of the given parabola.

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

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

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

Sketch the plane curve defined by the given parametric equations.

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

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

Graph the conic section with focus and the given directrix and eccentricity. Directrix

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 y = -1, e = 3

Which graph below corresponds to the given parametric equations?

Find the rectangular representation of the given polar point.

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

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

Sketch the plane curve defined by the given parametric equations.

Using the limit definition of integration, show that the area A bounded by the polar curve and the rays and is given by

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

Find all points of intersection of the two curves.

Find an equation for the indicated conic section. Parabola with focus (-6, 3) and directrix x = 0

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 vertex, focus, and directrix of the given parabola.

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

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

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

Sketch the plane curve defined by the given parametric equations.

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