Question 1

Identify the following quadric surface.

Accepted Answer

A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  elliptic paraboloid 
E)  ellipsoid 
A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  elliptic paraboloid 
E)  ellipsoid E

Question 2

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (2, 4, 5 ) and the plane   .

Accepted Answer

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

Question 3

Identify the equation of the following graph.

Accepted Answer

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

Question 4

Identify the following quadric surface.

Accepted Answer

A)  hyperboloid of two sheets 
B)  elliptic cone 
C)  ellipsoid 
D)  elliptic paraboloid 
E)  hyperboloid of one sheet 
A)  hyperboloid of two sheets 
B)  elliptic cone 
C)  ellipsoid 
D)  elliptic paraboloid 
E)  hyperboloid of one sheet

Question 5

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution

Accepted Answer

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

Question 6

Identify the following quadric surface.

Accepted Answer

A)  elliptic paraboloid 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  hyperboloid of one sheet 
E)  ellipsoid 
A)  elliptic paraboloid 
B)  elliptic cone 
C)  hyperboloid of two sheets 
D)  hyperboloid of one sheet 
E)  ellipsoid

Question 7

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve   in the yz-plane about the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell method to find its volume. Round your answer to one decimal place.

Accepted Answer

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

Question 8

Identify the following quadric surface.

Accepted Answer

A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of two sheets 
E)  hyperbolic paraboloid 
A)  hyperboloid of one sheet 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of two sheets 
E)  hyperbolic paraboloid

Question 9

Given the equation of a surface of revolution   find the equation of its generating curve in the yz-plane rotating about the y-axis.

Accepted Answer

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

Question 10

Identify the equation of the following graph.

Accepted Answer

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

Question 11

Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4739 miles and the polar radius is 4394 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the origin and that the trace formed by the plane   corresponds to the equator.)

Accepted Answer

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

Question 12

Find the length of the minor axis of the ellipse generated when the surface   is intersected by the plane   .

Accepted Answer

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

Question 13

Find an equation for the surface of revolution generated by revolving the curve   in the xz-plane about the z-axis.

Accepted Answer

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

Question 14

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve   in the yz-plane about the z-axis. Find an equation for the surface of revolution.

Accepted Answer

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

Question 15

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 16

Identify the following quadric surface.

Accepted Answer

A)  ellipsoid 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of one sheet 
E)  hyperboloid of two sheets 
A)  ellipsoid 
B)  elliptic cone 
C)  elliptic paraboloid 
D)  hyperboloid of one sheet 
E)  hyperboloid of two sheets

Question 17

Use the shell method to find the volume of the solid below the surface formed by revolving the curve   about the z-axis and above the xy-plane.

Accepted Answer

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

Question 18

Find an equation of a generating curve given the equation of its surface of revolution.   Equation of Curve Coordinate Plane
Axis of Revolution

Accepted Answer

A)    xz-plane z-axis 
B)    xz-plane z-axis 
C)    yz-plane y-axis 
D)    yz-plane z-axis 
E)    yz-plane y-axis 
A)    xz-plane z-axis 
B)    xz-plane z-axis 
C)    yz-plane y-axis 
D)    yz-plane z-axis 
E)    yz-plane y-axis

Question 19

Identify the following quadric surface.

Accepted Answer

A)  Elliptic cone 
B)  Hyperboloid of two sheets 
C)  Elliptic paraboloid 
D)  ellipsoid 
E)  Hyperboloid of one sheet 
A)  Elliptic cone 
B)  Hyperboloid of two sheets 
C)  Elliptic paraboloid 
D)  ellipsoid 
E)  Hyperboloid of one sheet

Question 20

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve   in the yz-plane about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.

Accepted Answer

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

Exam 11: Section 6: Vectors and the Geometry of Space

Identify the following quadric surface.

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (2, 4, 5 ) and the plane .

Identify the equation of the following graph.

Identify the following quadric surface.

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution

Identify the following quadric surface.

Identify the following quadric surface.

Given the equation of a surface of revolution find the equation of its generating curve in the yz-plane rotating about the y-axis.

Identify the equation of the following graph.

Find the length of the minor axis of the ellipse generated when the surface is intersected by the plane .

Find an equation for the surface of revolution generated by revolving the curve in the xz-plane about the z-axis.

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve in the yz-plane about the z-axis. Find an equation for the surface of revolution.

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution

Identify the following quadric surface.

Use the shell method to find the volume of the solid below the surface formed by revolving the curve about the z-axis and above the xy-plane.

Find an equation of a generating curve given the equation of its surface of revolution. Equation of Curve Coordinate Plane Axis of Revolution

Identify the following quadric surface.

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series

Section 5: Infinite Series

Section 6: Infinite Series