Question 1

Use the Integral Test to determine the convergence or divergence of the series. ​   ​

Accepted Answer

A) converges 
B) diverges 
C) Integral Test inconclusive 
A) converges 
B) diverges 
C) Integral Test inconclusive

Question 2

Write an expression for the nth term of the sequence   . ​

Accepted Answer

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

Question 3

Use the definition to find the Taylor series centered at   for the function   . ​

Accepted Answer

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

Question 4

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of   at   . ​

Accepted Answer

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

Question 5

Write the next two apparent terms of the sequence   . ​

Accepted Answer

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

Question 6

Determine whether the series   converges conditionally or absolutely,or diverges. ​

Accepted Answer

A) The series converges conditionally but does not converge absolutely. 
B) The series converges absolutely but does not converge conditionally. 
C) The series diverges. 
D) The series converges absolutely. 
A) The series converges conditionally but does not converge absolutely. 
B) The series converges absolutely but does not converge conditionally. 
C) The series diverges. 
D) The series converges absolutely.

Question 7

Find the Maclaurin polynomial of degree 4 for the function. ​   ​

Accepted Answer

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

Question 8

Find the Maclaurin polynomial of degree two for the function   . ​

Accepted Answer

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

Question 9

Find a power series for the function   centered at 0. ​

Accepted Answer

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

Question 10

The Maclaurin series for   ​.What is the Maclaurin series for   ? ​

Accepted Answer

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

Question 11

Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 4,000 units.Each year 10% of the units that have been sold will become inoperative.So,4,000 units will be in use after 1 year,   units will be in use after 2 years,and so on.How many units will be in use after n years? ​

Accepted Answer

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

Question 12

Which of the following series is absolutely convergent? ​

Accepted Answer

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

Question 13

Find the interval of convergence of the power series.(Be sure to include a check for convergence at the endpoints of the interval. ) ​   ​

Accepted Answer

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

Question 14

Find the third degree Taylor polynomial centered at   for the function. ​   ​

Accepted Answer

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

Question 15

Find all values of x for which the series converges.For these values of x,write the sum of the series as a function of x. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) The series diverges for all x.​ 
A)    
B)    
C)    
D)    
E) The series diverges for all x.​

Question 16

Use the Root Test to determine the convergence or divergence of the series   . ​

Accepted Answer

A) converges 
B) diverges 
A) converges 
B) diverges

Question 17

Use the Direct Comparison Test (if possible)to determine whether the series   converges or diverges. ​

Accepted Answer

A) diverges 
B) converges 
A) diverges 
B) converges

Question 18

Find the sum of the convergent series   by using a well-known function.Round your answer to four decimal places. ​

Accepted Answer

A) 0.3365 
B) 0.8755 
C) 1.6487 
D) 0.1823 
E) 1.6094 
A) 0.3365 
B) 0.8755 
C) 1.6487 
D) 0.1823 
E) 1.6094

Question 19

True or false: The series   diverges.
​

Accepted Answer

A) True 
 B)False

Question 20

True or false.The infinite series   .
​

Accepted Answer

A) True 
 B)False

Use the Integral Test to determine the convergence or divergence of the series.

Write an expression for the nth term of the sequence .

Use the definition to find the Taylor series centered at for the function .

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of at .

Write the next two apparent terms of the sequence .

Determine whether the series converges conditionally or absolutely,or diverges.

Find the Maclaurin polynomial of degree 4 for the function.

Find the Maclaurin polynomial of degree two for the function .

Find a power series for the function centered at 0.

The Maclaurin series for .What is the Maclaurin series for ?

Which of the following series is absolutely convergent?

Find the interval of convergence of the power series.(Be sure to include a check for convergence at the endpoints of the interval. )

Find the third degree Taylor polynomial centered at for the function.

Find all values of x for which the series converges.For these values of x,write the sum of the series as a function of x.

Use the Root Test to determine the convergence or divergence of the series .

Use the Direct Comparison Test (if possible)to determine whether the series converges or diverges.

Find the sum of the convergent series by using a well-known function.Round your answer to four decimal places.

True or false: The series diverges.

True or false.The infinite series .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 9: Infinite Series

Use the Integral Test to determine the convergence or divergence of the series. ​ ​

Write an expression for the nth term of the sequence . ​

Use the definition to find the Taylor series centered at for the function . ​

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of at . ​

Write the next two apparent terms of the sequence . ​

Determine whether the series converges conditionally or absolutely,or diverges. ​

Find the Maclaurin polynomial of degree 4 for the function. ​ ​

Find the Maclaurin polynomial of degree two for the function . ​

Find a power series for the function centered at 0. ​

The Maclaurin series for ​.What is the Maclaurin series for ? ​

Which of the following series is absolutely convergent? ​

Find the interval of convergence of the power series.(Be sure to include a check for convergence at the endpoints of the interval. ) ​ ​

Find the third degree Taylor polynomial centered at for the function. ​ ​

Find all values of x for which the series converges.For these values of x,write the sum of the series as a function of x. ​ ​

Use the Root Test to determine the convergence or divergence of the series . ​

Use the Direct Comparison Test (if possible)to determine whether the series converges or diverges. ​

Find the sum of the convergent series by using a well-known function.Round your answer to four decimal places. ​

True or false: The series diverges. ​

True or false.The infinite series . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Use the Integral Test to determine the convergence or divergence of the series.

Write an expression for the nth term of the sequence .

Use the definition to find the Taylor series centered at for the function .

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of at .

Write the next two apparent terms of the sequence .

Determine whether the series converges conditionally or absolutely,or diverges.

Find the Maclaurin polynomial of degree 4 for the function.

Find the Maclaurin polynomial of degree two for the function .

Find a power series for the function centered at 0.

The Maclaurin series for .What is the Maclaurin series for ?

Which of the following series is absolutely convergent?

Find the interval of convergence of the power series.(Be sure to include a check for convergence at the endpoints of the interval. )

Find the third degree Taylor polynomial centered at for the function.

Find all values of x for which the series converges.For these values of x,write the sum of the series as a function of x.

Use the Root Test to determine the convergence or divergence of the series .

Use the Direct Comparison Test (if possible)to determine whether the series converges or diverges.

Find the sum of the convergent series by using a well-known function.Round your answer to four decimal places.

True or false: The series diverges.

True or false.The infinite series .