Question 1

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

Accepted Answer

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

Question 2

Use a graphing utility to graph   and P1,a first-degree polynomial function whose value and slope agree with the value and slope of f at   . ​

Accepted Answer

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

Question 3

Determine the convergence or divergence of the series using any appropriate test from this chapter.Identify the test used. ​   ​

Accepted Answer

A) diverges;both Ratio Test and Theorem 9.9 (nth Term Test for Divergence) 
B) converges;Integral Test 
C) diverges;Theorem 9.9 (nth Term Test for Divergence) 
D) converges;p-series 
E) diverges;Ratio Test 
A) diverges;both Ratio Test and Theorem 9.9 (nth Term Test for Divergence) 
B) converges;Integral Test 
C) diverges;Theorem 9.9 (nth Term Test for Divergence) 
D) converges;p-series 
E) diverges;Ratio Test

Question 4

The terms of a series   are defined recursively.Determine the convergence or divergence of the series.Explain your reasoning. ​   ,   ​

Accepted Answer

A) diverges;Ratio Test 
B) converges;Ratio Test 
C) converges;Integral Test 
D) diverges;Alternating Series Test 
E) diverges;Root Test 
A) diverges;Ratio Test 
B) converges;Ratio Test 
C) converges;Integral Test 
D) diverges;Alternating Series Test 
E) diverges;Root Test

Question 5

Suppose the annual spending by tourists in a resort city is $200 million.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the same city,and so on.Summing all of this spending indefinitely,leads to the geometric series   .Find the sum of this series. ​

Accepted Answer

A) $1,600 million 
B) $801 million 
C) $400 million 
D) $1,601 million 
E) $800 million 
A) $1,600 million 
B) $801 million 
C) $400 million 
D) $1,601 million 
E) $800 million

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

True or false: The series   converges.
​

Accepted Answer

A) True 
 B)False

Question 9

Find the values of x for which the series   converges. ​

Accepted Answer

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

Question 10

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Compute the budget after the fourth year.Round your answer to the nearest integer.

Accepted Answer

A) $1,433,600,000 
B) $165,995,062 
C) $89,600,000 
D) $1,012,217,284 
E) $453,600,000 
A) $1,433,600,000 
B) $165,995,062 
C) $89,600,000 
D) $1,012,217,284 
E) $453,600,000

Question 11

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.   ​

Accepted Answer

A) 4 
B) 2 
C) 5 
D) 7 
E) 3 
A) 4 
B) 2 
C) 5 
D) 7 
E) 3

Question 12

Use the power series   to determine a power series centered at 0 for the function   . ​

Accepted Answer

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

Question 13

Find the positive values of p for which the series   converges. ​

Accepted Answer

A) The series converges for   . 
B) The series converges for   . 
C) The series diverges for all positive values of p. 
D) The series converges for   . 
E) The series converges for   . 
A) The series converges for   . 
B) The series converges for   . 
C) The series diverges for all positive values of p. 
D) The series converges for   . 
E) The series converges for   .

Question 14

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 15

Use the series   for   to approximate the value of   using   .Round your answer to three decimal places. ​

Accepted Answer

A) 0.245 
B) 0.195 
C) 0.328 
D) 0.161 
E) 0.281 
A) 0.245 
B) 0.195 
C) 0.328 
D) 0.161 
E) 0.281

Question 16

True or false: The series   diverges.
​

Accepted Answer

A) True 
 B)False

Question 17

Determine the convergence or divergence of the series. ​   ​

Accepted Answer

A) diverges 
B) converges 
C) cannot be determined 
A) diverges 
B) converges 
C) cannot be determined

Question 18

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

Accepted Answer

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

Question 19

Determine the convergence or divergence of the sequence with the given nth term.If the sequence converges,find its limit. ​   ​

Accepted Answer

A) The sequence converges to -1. 
B) The sequence converges to 0. 
C) The sequence diverges. 
D) The sequence converges to 1. 
E) The sequence diverges to 1. 
A) The sequence converges to -1. 
B) The sequence converges to 0. 
C) The sequence diverges. 
D) The sequence converges to 1. 
E) The sequence diverges to 1.

Question 20

Identify the most appropriate test to be used to determine whether the series   converges or diverges. ​

Accepted Answer

A) Limit Comparison Test with   
B) Direct Comparison Test with   
C) Alternating Series Test 
D) Root Test 
E) Ratio Test 
A) Limit Comparison Test with   
B) Direct Comparison Test with   
C) Alternating Series Test 
D) Root Test 
E) Ratio Test

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

Use a graphing utility to graph and P₁,a first-degree polynomial function whose value and slope agree with the value and slope of f at .

Determine the convergence or divergence of the series using any appropriate test from this chapter.Identify the test used.

The terms of a series are defined recursively.Determine the convergence or divergence of the series.Explain your reasoning. ,

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

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

True or false: The series converges.

Find the values of x for which the series converges.

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Compute the budget after the fourth year.Round your answer to the nearest integer.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.

Use the power series to determine a power series centered at 0 for the function .

Find the positive values of p for which the series converges.

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

Use the series for to approximate the value of using .Round your answer to three decimal places.

True or false: The series diverges.

Determine the convergence or divergence of the series.

Find a power series for the function centered at 0.

Determine the convergence or divergence of the sequence with the given nth term.If the sequence converges,find its limit.

Identify the most appropriate test to be used to determine whether the series converges or diverges.

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 Ratio Test to determine the convergence or divergence of the series. ​ ​

Use a graphing utility to graph and P1,a first-degree polynomial function whose value and slope agree with the value and slope of f at . ​

Determine the convergence or divergence of the series using any appropriate test from this chapter.Identify the test used. ​ ​

The terms of a series are defined recursively.Determine the convergence or divergence of the series.Explain your reasoning. ​ , ​

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

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

True or false: The series converges. ​

Find the values of x for which the series converges. ​

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Compute the budget after the fourth year.Round your answer to the nearest integer.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005. ​

Use the power series to determine a power series centered at 0 for the function . ​

Find the positive values of p for which the series converges. ​

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

Use the series for to approximate the value of using .Round your answer to three decimal places. ​

True or false: The series diverges. ​

Determine the convergence or divergence of the series. ​ ​

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

Determine the convergence or divergence of the sequence with the given nth term.If the sequence converges,find its limit. ​ ​

Identify the most appropriate test to be used to determine whether the series converges or diverges. ​

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 Ratio Test to determine the convergence or divergence of the series.

Use a graphing utility to graph and P₁,a first-degree polynomial function whose value and slope agree with the value and slope of f at .

Determine the convergence or divergence of the series using any appropriate test from this chapter.Identify the test used.

The terms of a series are defined recursively.Determine the convergence or divergence of the series.Explain your reasoning. ,

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

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

True or false: The series converges.

Find the values of x for which the series converges.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.

Use the power series to determine a power series centered at 0 for the function .

Find the positive values of p for which the series converges.

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

Use the series for to approximate the value of using .Round your answer to three decimal places.

True or false: The series diverges.

Determine the convergence or divergence of the series.

Find a power series for the function centered at 0.

Determine the convergence or divergence of the sequence with the given nth term.If the sequence converges,find its limit.

Identify the most appropriate test to be used to determine whether the series converges or diverges.