Question 1

Find the area of the surface generated by revolving the curve about the given axis.   (i) x-axis; (ii) y-axis

Accepted Answer

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

Question 2

Find the arc length of the curve   on the interval   . Round your answer to three decimal places.

Accepted Answer

A)  287.453 
B)  191.635 
C)  193.606 
D)  66.480 
E)  99.721 
A)  287.453 
B)  191.635 
C)  193.606 
D)  66.480 
E)  99.721 B

Question 3

Find the arc length of the curve on the given interval.

Accepted Answer

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

Question 4

Determine the t intervals on which the curve   is concave downward or concave upward.

Accepted Answer

A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   
D)  concave upward:   
E)  concave downward:   
A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   
D)  concave upward:   
E)  concave downward:

Question 5

Find   and   if possible, and find the slope and concavity (if possible) at the point corresponding to   .

Accepted Answer

A)    at   : slope 1 and concave down 
B)    at   : slope   and concave down 
C)    at   : slope   and concave up 
D)    at   : slope 1 and concave up 
E)    at   : slope of   and concave down 
A)    at   : slope 1 and concave down 
B)    at   : slope   and concave down 
C)    at   : slope   and concave up 
D)    at   : slope 1 and concave up 
E)    at   : slope of   and concave down

Question 6

Find the second derivative   of the parametric equations   . Round your answer to two decimal places, if necessary.

Accepted Answer

A)  0 
B)  2.00 
C)    
D)  0.50 
E)    
A)  0 
B)  2.00 
C)    
D)  0.50 
E)

Question 7

The path of a projectile is modeled by the parametric equations   and   where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.

Accepted Answer

A)  387.2 ft 
B)  595.8 ft 
C)  335.0 ft 
D)  269.9 ft 
E)  465.4 ft 
A)  387.2 ft 
B)  595.8 ft 
C)  335.0 ft 
D)  269.9 ft 
E)  465.4 ft

Question 8

Find the area of the surface generated by revolving the curve   about the x-axis on the interval   .

Accepted Answer

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

Question 9

Determine the t intervals on which the curve   is concave downward or concave upward.

Accepted Answer

A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   ; concave upward:   
D)  concave downward:   ; concave upward:   
E)  concave downward:   ; concave upward:   
A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   ; concave upward:   
D)  concave downward:   ; concave upward:   
E)  concave downward:   ; concave upward:

Question 10

Find the area of the surface generated by revolving the curve   about the y-axis on the interval   . Round your answer to two decimal places.

Accepted Answer

A)  1427.12 
B)  1178.96 
C)  1049.37 
D)  589.48 
E)  1898.04 
A)  1427.12 
B)  1178.96 
C)  1049.37 
D)  589.48 
E)  1898.04

Question 11

Find the arc length of the curve on the given interval.

Accepted Answer

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

Question 12

Find all points (if any) of horizontal and vertical tangency to the curve   .

Accepted Answer

A)  horizontal tangents:   , vertical tangent: none 
B)  horizontal tangent: none, vertical tangents:   
C)  horizontal tangents:   , vertical tangent: none 
D)  horizontal tangent: none, vertical tangents:   
E)  horizontal tangent: none, vertical tangent: none 
A)  horizontal tangents:   , vertical tangent: none 
B)  horizontal tangent: none, vertical tangents:   
C)  horizontal tangents:   , vertical tangent: none 
D)  horizontal tangent: none, vertical tangents:   
E)  horizontal tangent: none, vertical tangent: none

Question 13

Find an equation of the tangent line at a point   on the curve   .

Accepted Answer

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

Question 14

Find the arc length of the curve on the given interval.

Accepted Answer

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

Question 15

Find   .

Accepted Answer

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

Question 16

Find the second derivative   of the parametric equations   .

Accepted Answer

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

Question 17

The path of a projectile is modeled by the parametric equations   and   where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.

Accepted Answer

A)  312.85 ft 
B)  521.42 ft 
C)  131.09 ft 
D)  391.06 ft 
E)  195.53 ft 
A)  312.85 ft 
B)  521.42 ft 
C)  131.09 ft 
D)  391.06 ft 
E)  195.53 ft

Question 18

Find   and   if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5.

Accepted Answer

A)    : slope   and concave up 
B)    slope -6 and concave down 
C)    slope 14 and concave up 
D)    : slope 6 and concave down 
E)    : slope   and concave up 
A)    : slope   and concave up 
B)    slope -6 and concave down 
C)    slope 14 and concave up 
D)    : slope 6 and concave down 
E)    : slope   and concave up

Question 19

Find all points (if any) of horizontal and vertical tangency to the curve   .

Accepted Answer

A)  horizontal tangents:   , vertical tangents:   
B)  horizontal tangents:   , vertical tangents:   
C)  horizontal tangent:   , vertical tangent:   
D)  horizontal tangents:   , vertical tangents:   
E)  horizontal tangent:   , vertical tangent:   
A)  horizontal tangents:   , vertical tangents:   
B)  horizontal tangents:   , vertical tangents:   
C)  horizontal tangent:   , vertical tangent:   
D)  horizontal tangents:   , vertical tangents:   
E)  horizontal tangent:   , vertical tangent:

Question 20

Find the area of the surface generated by revolving the curve about the given axis.   (i) x-axis; (ii) y-axis

Accepted Answer

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

Exam 10: Section 3: Conics, Parametric Equations, and Polar Coordinates

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

Find the arc length of the curve on the interval . Round your answer to three decimal places.

Find the arc length of the curve on the given interval.

Determine the t intervals on which the curve is concave downward or concave upward.

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to .

Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.

Find the area of the surface generated by revolving the curve about the x-axis on the interval .

Determine the t intervals on which the curve is concave downward or concave upward.

Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places.

Find the arc length of the curve on the given interval.

Find all points (if any) of horizontal and vertical tangency to the curve .

Find an equation of the tangent line at a point on the curve .

Find the arc length of the curve on the given interval.

Find .

Find the second derivative of the parametric equations .

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5.

Find all points (if any) of horizontal and vertical tangency to the curve .

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

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