Question 1

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

Accepted Answer

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

Question 2

Find rectangular coordinates for the given polar point.

Accepted Answer

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

Question 3

Identify all values of   where r = 0.

Accepted Answer

A)    
B)    
C)    
D)  no solution 
A)    
B)    
C)    
D)  no solution

Question 4

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

Accepted Answer

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

Question 5

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)  6.6855k 
B)  2.5546k 
C)  11.7447k 
D)  7.8653k 
A)  6.6855k 
B)  2.5546k 
C)  11.7447k 
D)  7.8653k

Question 6

A medical procedure called shockwave lithotripsy is used to break up kidney stones that are too large or irregular to be passed. In this procedure, shockwaves emanating from a transducer located at the other focus. Suppose that the reflector is described by the equation   (in units of inches), how far from the kidney stone should the transducer be placed?

Accepted Answer

A)  7 in. 
B)  49 in. 
C)  11 in. 
D)  13 in. 
A)  7 in. 
B)  49 in. 
C)  11 in. 
D)  13 in.

Question 7

Which graph below corresponds to the given parametric equations?

Accepted Answer

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

Question 8

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

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

Question 10

Find the arc length of the given curve.

Accepted Answer

A)  9 
B)  24 
C)    
D)    
A)  9 
B)  24 
C)    
D)

Question 11

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -5, e = 4

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find rectangular coordinates for the given polar point.

Accepted Answer

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

Question 14

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 2, e = 0.5

Accepted Answer

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

Question 15

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

Accepted Answer

Answers ma

Question 16

Which graph below corresponds to the given parametric equations?

Accepted Answer

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

Question 17

Interpret and graph the conic section.

Accepted Answer

The graph is a hyper

Question 18

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

Accepted Answer

A)  7.667 
B)  6.787 
C)  3.005 
D)  8.445 
A)  7.667 
B)  6.787 
C)  3.005 
D)  8.445

Question 19

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

Question 20

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

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

Find rectangular coordinates for the given polar point.

Identify all values of where r = 0.

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

Which graph below corresponds to the given parametric equations?

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

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

Find the arc length of the given curve.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -5, e = 4

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

Find rectangular coordinates for the given polar point.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 2, e = 0.5

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

Which graph below corresponds to the given parametric equations?

Interpret and graph the conic section.

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

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

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

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 all points at which |r| is a maximum.

Find rectangular coordinates for the given polar point.

Identify all values of where r = 0.

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

Which graph below corresponds to the given parametric equations?

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

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

Find the arc length of the given curve.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix x = -5, e = 4

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

Find rectangular coordinates for the given polar point.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 2, e = 0.5

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

Which graph below corresponds to the given parametric equations?

Interpret and graph the conic section.

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

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

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

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