Question 1

​What are all values of a for which the series   converges? ​

Accepted Answer

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

Question 2

Use the Direct Comparison Test (if possible)to determine whether the series   ​

Accepted Answer

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

Question 3

Use a power series to approximate the value of the integral   with an error of less than 0.01.Round your answer to two decimal places. ​

Accepted Answer

A) 0.88 
B) 0.84 
C) 0.81 
D) 0.74 
E) 0.89 
A) 0.88 
B) 0.84 
C) 0.81 
D) 0.74 
E) 0.89

Question 4

Find the values of x for which the series   converges.

Accepted Answer

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

Question 5

State where the power series   is centered. ​

Accepted Answer

A) 0 
B) -2 
C) 7 
D) 2 
E) -7 
A) 0 
B) -2 
C) 7 
D) 2 
E) -7

Question 6

Determine the values of x for which the function   can be replaced by the Taylor polynomial   if the error cannot exceed 0.004.Round your answer to four decimal places. ​

Accepted Answer

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

Question 7

True or false: The series   converges.
​

Accepted Answer

A) True 
 B)False

Question 8

Consider the sequence   whose nth term is given by   where P is the principal,   is the account balance in dollars after n months,and r is the interest rate compounded annually.Find the ninth term of the sequence if   and   .Round your answer to two decimal places. ​

Accepted Answer

A) $9,898.12 
B) $10,875.05 
C) $10,214.72 
D) $9,590.28 
E) $9,712.38 
A) $9,898.12 
B) $10,875.05 
C) $10,214.72 
D) $9,590.28 
E) $9,712.38

Question 9

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

Accepted Answer

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

Question 10

Find a geometric power series for the function centered at 0, (i)by the technique shown in Examples 1 and 2 and (ii)by long division. ​   ​

Accepted Answer

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

Question 11

Which value is smaller,   ​ Give a reason for your answer.

Accepted Answer

​Because @#IMG-DLM& is an alternating se

Question 12

Use a power series to approximate the value of the integral   with an error less than 0.001.Round your answer to four decimal places. ​

Accepted Answer

A) 0.4715 
B) 0.4300 
C) 0.4507 
D) 0.4730 
E) 0.4515 
A) 0.4715 
B) 0.4300 
C) 0.4507 
D) 0.4730 
E) 0.4515

Question 13

Consider the function   and its second-degree polynomial   at   .Compute the value of   and   Round your answer to four decimal places. ​

Accepted Answer

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

Question 14

Match the sequence with its graph. ​   ​

Accepted Answer

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

Question 15

Determine the convergence or divergence of the series   . ​

Accepted Answer

A) The series   diverges. 
B) The series   converges. 
A) The series   diverges. 
B) The series   converges.

Question 16

Find the sum of the convergent series   . ​

Accepted Answer

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

Question 17

Find the differential equation having the solution   . ​

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Find the radius of convergence of the power series. ​   ​

Accepted Answer

A)    
B) 8 
C) 16 
D) 0 
E) 4 
A)    
B) 8 
C) 16 
D) 0 
E) 4

Question 20

Determine the convergence or divergence of the series   . ​

Accepted Answer

A) The series   converges. 
B) The series   diverges. 
A) The series   converges. 
B) The series   diverges.

What are all values of a for which the series converges?

Use the Direct Comparison Test (if possible)to determine whether the series

Use a power series to approximate the value of the integral with an error of less than 0.01.Round your answer to two decimal places.

Find the values of x for which the series converges.

State where the power series is centered.

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.004.Round your answer to four decimal places.

True or false: The series converges.

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months,and r is the interest rate compounded annually.Find the ninth term of the sequence if and .Round your answer to two decimal places.

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

Find a geometric power series for the function centered at 0, (i)by the technique shown in Examples 1 and 2 and (ii)by long division.

Which value is smaller, Give a reason for your answer.

Use a power series to approximate the value of the integral with an error less than 0.001.Round your answer to four decimal places.

Consider the function and its second-degree polynomial at .Compute the value of and Round your answer to four decimal places.

Match the sequence with its graph.

Determine the convergence or divergence of the series .

Find the sum of the convergent series .

Find the differential equation having the solution .

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

Find the radius of convergence of the power series.

Determine the convergence or divergence of the 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

​What are all values of a for which the series converges? ​

Use the Direct Comparison Test (if possible)to determine whether the series ​

Use a power series to approximate the value of the integral with an error of less than 0.01.Round your answer to two decimal places. ​

Find the values of x for which the series converges.

State where the power series is centered. ​

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.004.Round your answer to four decimal places. ​

True or false: The series converges. ​

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months,and r is the interest rate compounded annually.Find the ninth term of the sequence if and .Round your answer to two decimal places. ​

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

Find a geometric power series for the function centered at 0, (i)by the technique shown in Examples 1 and 2 and (ii)by long division. ​ ​

Which value is smaller, ​ Give a reason for your answer.

Use a power series to approximate the value of the integral with an error less than 0.001.Round your answer to four decimal places. ​

Consider the function and its second-degree polynomial at .Compute the value of and Round your answer to four decimal places. ​

Match the sequence with its graph. ​ ​

Determine the convergence or divergence of the series . ​

Find the sum of the convergent series . ​

Find the differential equation having the solution . ​

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

Find the radius of convergence of the power series. ​ ​

Determine the convergence or divergence of the 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

What are all values of a for which the series converges?

Use the Direct Comparison Test (if possible)to determine whether the series

Use a power series to approximate the value of the integral with an error of less than 0.01.Round your answer to two decimal places.

State where the power series is centered.

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.004.Round your answer to four decimal places.

True or false: The series converges.

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months,and r is the interest rate compounded annually.Find the ninth term of the sequence if and .Round your answer to two decimal places.

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

Find a geometric power series for the function centered at 0, (i)by the technique shown in Examples 1 and 2 and (ii)by long division.

Which value is smaller, Give a reason for your answer.

Use a power series to approximate the value of the integral with an error less than 0.001.Round your answer to four decimal places.

Consider the function and its second-degree polynomial at .Compute the value of and Round your answer to four decimal places.

Match the sequence with its graph.

Determine the convergence or divergence of the series .

Find the sum of the convergent series .

Find the differential equation having the solution .

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

Find the radius of convergence of the power series.

Determine the convergence or divergence of the series .