Question 1

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 2

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

Accepted Answer

A)  vertex (-7, 8); focus   ; directrix   
B)  vertex (8, -7); focus   ; directrix   
C)  vertex   ; focus (8, -7); directrix   
D)  vertex (8, -7); focus   ; directrix   
A)  vertex (-7, 8); focus   ; directrix   
B)  vertex (8, -7); focus   ; directrix   
C)  vertex   ; focus (8, -7); directrix   
D)  vertex (8, -7); focus   ; directrix

Question 3

Find a polar equation corresponding to the given rectangular equation. x = 2

Accepted Answer

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

Question 4

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 5

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 6

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 3, e = 0.3

Accepted Answer

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

Question 7

Find an equation for the indicated conic section. Hyperbola with foci (1, 24), (1, -26) and vertices (1, -8), (1, 6)

Accepted Answer

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

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

Which graph below corresponds to the given parametric equations?

Accepted Answer

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

Question 10

Find the area enclosed by the given curve.

Accepted Answer

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

Question 11

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

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

Question 12

Find a corresponding x-y equation.

Accepted Answer

A)    
B)    
C)  x = 5 
D)  x2 + y2 = 5 
A)    
B)    
C)  x = 5 
D)  x2 + y2 = 5

Question 13

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

Accepted Answer

A)    
B)  (1,0) 
C)    
D)    
A)    
B)  (1,0) 
C)    
D)

Question 14

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 15

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 16

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 17

Find the rectangular representation of the given polar point.

Accepted Answer

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

Question 18

Find parametric equations for the path of a projectile launched from height   ft with initial speed   ft/s at angle   from the horizontal.

Accepted Answer

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

Question 19

Find an equation for the indicated conic section. Parabola with focus (-2, 2) and directrix x = -8

Accepted Answer

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

Question 20

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

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

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

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

Find a polar equation corresponding to the given rectangular equation. x = 2

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

Find the rectangular representation of the given polar point.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 3, e = 0.3

Find an equation for the indicated conic section. Hyperbola with foci (1, 24), (1, -26) and vertices (1, -8), (1, 6)

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].

Which graph below corresponds to the given parametric equations?

Find the area enclosed by the given curve.

Sketch the plane curve defined by the given parametric equations.

Find a corresponding x-y equation.

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

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.

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 rectangular representation of the given polar point.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.

Find an equation for the indicated conic section. Parabola with focus (-2, 2) and directrix x = -8

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

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

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

Find a polar equation corresponding to the given rectangular equation. x = 2

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

Find the rectangular representation of the given polar point.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = 3, e = 0.3

Find an equation for the indicated conic section. Hyperbola with foci (1, 24), (1, -26) and vertices (1, -8), (1, 6)

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].

Which graph below corresponds to the given parametric equations?

Find the area enclosed by the given curve.

Sketch the plane curve defined by the given parametric equations.

Find a corresponding x-y equation.

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

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.

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 rectangular representation of the given polar point.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.

Find an equation for the indicated conic section. Parabola with focus (-2, 2) and directrix x = -8

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

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