Question 1

Evaluate the   using L'Hôpital's Rule if necessary. ​

Accepted Answer

A)    
B)    
C)    
D) 0 
E)    
A)    
B)    
C)    
D) 0 
E)

Question 2

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 3

Determine whether the improper integral   diverges or converges.Evaluate the integral if it converges. ​

Accepted Answer

A) 90 
B) 27 
C)    
D) 9 
E) diverges 
A) 90 
B) 27 
C)    
D) 9 
E) diverges

Question 4

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 5

Evaluate the limit   first by using techniques from Chapter 1 then by using L'Hopital's Rule. ​

Accepted Answer

A)    
B) 0 
C)    
D)    
E) does not exist 
A)    
B) 0 
C)    
D)    
E) does not exist

Question 6

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 7

Evaluate the definite integral   . ​

Accepted Answer

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

Question 8

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 9

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 10

Find the indefinite integral by making the substitution   . ​   ​

Accepted Answer

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

Question 11

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 12

Evaluate the definite integral   . ​

Accepted Answer

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

Question 13

Find the area between the x-axis and the graph of the function   . ​   ​

Accepted Answer

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

Question 14

Evaluate the definite integral   . ​

Accepted Answer

A) 1 
B) 5 
C) 2 
D) 0 
E) 6 
A) 1 
B) 5 
C) 2 
D) 0 
E) 6

Question 15

Solve the differential equation   . ​

Accepted Answer

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

Question 16

​What is the area of the region in the first quadrant between the   -axis,   -axis,   ,and   ? ​   ​

Accepted Answer

A) ​2 
B) ​3 
C) ​1 
D) ​∞ 
A) ​2 
B) ​3 
C) ​1 
D) ​∞

Question 17

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 18

Suppose the capitalized cost C is given by   ,where   is the original investment,t is the time in years,r is the annual interest rate compounded continuously,and   is the annual cost of maintenance.Find the capitalized cost C of an asset forever if   ,   ,and   .Round your answer to the nearest dollar. ​

Accepted Answer

A) $1,031,414 
B) $661,820 
C) $1,031,443 
D) $1,031,429 
E) $687,820 
A) $1,031,414 
B) $661,820 
C) $1,031,443 
D) $1,031,429 
E) $687,820

Question 19

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by   .Find the average value of y on the interval from   to   .Round your answer to three decimal places. ​

Accepted Answer

A) 1.125 
B) 0.318 
C) 0.286 
D) 0.358 
E) 0.900 
A) 1.125 
B) 0.318 
C) 0.286 
D) 0.358 
E) 0.900

Question 20

Determine whether the improper integral   diverges or converges.Evaluate the integral if it converges. ​

Accepted Answer

A) 49 
B) 13 
C)    
D)    
E) diverges 
A) 49 
B) 13 
C)    
D)    
E) diverges

Evaluate the using L'Hôpital's Rule if necessary.

Find the indefinite integral by making the substitution .

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Find the indefinite integral.

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule.

Find the indefinite integral.

Evaluate the definite integral .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Evaluate the definite integral .

Find the area between the x-axis and the graph of the function .

Evaluate the definite integral .

Solve the differential equation .

What is the area of the region in the first quadrant between the -axis, -axis, ,and ?

Find the indefinite integral.

Suppose the capitalized cost C is given by ,where is the original investment,t is the time in years,r is the annual interest rate compounded continuously,and is the annual cost of maintenance.Find the capitalized cost C of an asset forever if , ,and .Round your answer to the nearest dollar.

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by .Find the average value of y on the interval from to .Round your answer to three decimal places.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 8: Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Evaluate the using L'Hôpital's Rule if necessary. ​

Find the indefinite integral by making the substitution . ​ ​

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. ​

Find the indefinite integral. ​ ​

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule. ​

Find the indefinite integral. ​ ​

Evaluate the definite integral . ​

Find the indefinite integral. ​ ​

Find the indefinite integral. ​ ​

Find the indefinite integral by making the substitution . ​ ​

Find the indefinite integral. ​ ​

Evaluate the definite integral . ​

Find the area between the x-axis and the graph of the function . ​ ​

Evaluate the definite integral . ​

Solve the differential equation . ​

​What is the area of the region in the first quadrant between the -axis, -axis, ,and ? ​ ​

Find the indefinite integral. ​ ​

Suppose the capitalized cost C is given by ,where is the original investment,t is the time in years,r is the annual interest rate compounded continuously,and is the annual cost of maintenance.Find the capitalized cost C of an asset forever if , ,and .Round your answer to the nearest dollar. ​

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by .Find the average value of y on the interval from to .Round your answer to three decimal places. ​

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Evaluate the using L'Hôpital's Rule if necessary.

Find the indefinite integral by making the substitution .

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Find the indefinite integral.

Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule.

Find the indefinite integral.

Evaluate the definite integral .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Evaluate the definite integral .

Find the area between the x-axis and the graph of the function .

Evaluate the definite integral .

Solve the differential equation .

What is the area of the region in the first quadrant between the -axis, -axis, ,and ?

Find the indefinite integral.

Suppose the capitalized cost C is given by ,where is the original investment,t is the time in years,r is the annual interest rate compounded continuously,and is the annual cost of maintenance.Find the capitalized cost C of an asset forever if , ,and .Round your answer to the nearest dollar.

Suppose a damping force affects the vibration of a spring so that the displacement of the string is given by .Find the average value of y on the interval from to .Round your answer to three decimal places.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.