Question 1

Use the Direct Comparison Test to 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 2

If the first five terms of the Taylor expansion for   about   are   ,then   ​

Accepted Answer

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

Question 3

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 4

Find the Maclaurian series for the function     . ​

Accepted Answer

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

Question 5

The radius of convergence of the power series   ​. ​

Accepted Answer

A) ​3 
B) ​5 
C) ​4 
D) ​6 
A) ​3 
B) ​5 
C) ​4 
D) ​6

Question 6

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

Accepted Answer

A) diverges 
B) converges 
C) Limit Comparison Test does not apply 
A) diverges 
B) converges 
C) Limit Comparison Test does not apply

Question 7

Consider the function given by   .Find the interval of convergence for   . ​

Accepted Answer

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

Question 8

True or false: The series   converges.
​

Accepted Answer

A) True 
 B)False

Question 9

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.   ​

Accepted Answer

A) 5 
B) 4 
C) 2 
D) 6 
E) 3 
A) 5 
B) 4 
C) 2 
D) 6 
E) 3

Question 10

Graph the sequence   . ​

Accepted Answer

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

Question 11

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 12

True or false: The series   diverges .
​

Accepted Answer

A) True 
 B)False

Question 13

Write the first five terms of the sequence. ​   ​

Accepted Answer

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

Question 14

Evaluate   using the formula   where k is a real number,n is a positive integer,and   . ​

Accepted Answer

A) 14 
B) 16 
C) 10 
D) 4 
E) 6 
A) 14 
B) 16 
C) 10 
D) 4 
E) 6

Question 15

Determine the convergence or divergence of the series   using any appropriate test. ​

Accepted Answer

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

Question 16

Explain how to use the geometric series   to find the series for the function   . ​

Accepted Answer

A) replace x with   
B) replace x with   and multiply the series by
  
C) replace x with   and divide the series by
  
D) replace x with   and divide the series by
  
E) replace x with   
A) replace x with   
B) replace x with   and multiply the series by
  
C) replace x with   and divide the series by
  
D) replace x with   and divide the series by
  
E) replace x with

Question 17

Which of the following series is the power series expansion for   ​.

Accepted Answer

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

Question 18

Match the sequence with its graph. ​   ​

Accepted Answer

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

Question 19

Use the polynomial test to determine whether the series   converges or diverges. ​

Accepted Answer

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

Question 20

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)    ​

Use the Direct Comparison Test to determine the convergence or divergence of the series .

If the first five terms of the Taylor expansion for about are ,then

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

Find the Maclaurian series for the function .

The radius of convergence of the power series .

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

Consider the function given by .Find the interval of convergence for .

True or false: The series converges.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.

Graph the sequence .

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

True or false: The series diverges .

Write the first five terms of the sequence.

Evaluate using the formula where k is a real number,n is a positive integer,and .

Determine the convergence or divergence of the series using any appropriate test.

Explain how to use the geometric series to find the series for the function .

Which of the following series is the power series expansion for .

Match the sequence with its graph.

Use the polynomial test to determine whether the series converges or diverges.

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

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 Direct Comparison Test to determine the convergence or divergence of the series . ​

If the first five terms of the Taylor expansion for about are ,then ​

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

Find the Maclaurian series for the function . ​

The radius of convergence of the power series ​. ​

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

Consider the function given by .Find the interval of convergence for . ​

True or false: The series converges. ​

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007. ​

Graph the sequence . ​

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

True or false: The series diverges . ​

Write the first five terms of the sequence. ​ ​

Evaluate using the formula where k is a real number,n is a positive integer,and . ​

Determine the convergence or divergence of the series using any appropriate test. ​

Explain how to use the geometric series to find the series for the function . ​

Which of the following series is the power series expansion for ​.

Match the sequence with its graph. ​ ​

Use the polynomial test to determine whether the series converges or diverges. ​

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

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 Direct Comparison Test to determine the convergence or divergence of the series .

If the first five terms of the Taylor expansion for about are ,then

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

Find the Maclaurian series for the function .

The radius of convergence of the power series .

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

Consider the function given by .Find the interval of convergence for .

True or false: The series converges.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.

Graph the sequence .

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

True or false: The series diverges .

Write the first five terms of the sequence.

Evaluate using the formula where k is a real number,n is a positive integer,and .

Determine the convergence or divergence of the series using any appropriate test.

Explain how to use the geometric series to find the series for the function .

Which of the following series is the power series expansion for .

Match the sequence with its graph.

Use the polynomial test to determine whether the series converges or diverges.

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