Question 1

Write the first five terms of the sequence of partial sums. ​   ​

Accepted Answer

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

Question 2

Identify the interval of convergence of a power series   . ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function   to be less than 0.001. ​

Accepted Answer

A) 3 
B) 2 
C) 5 
D) 1 
E) 4 
A) 3 
B) 2 
C) 5 
D) 1 
E) 4

Question 5

True or false: The series   converges.
​

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

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

Question 7

If   ​,the first three terms of the Taylor series expansion about   for   are ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Consider the series   .The sum of the series is   Find the sum of the series   . ​

Accepted Answer

A) 0.0095 
B) 0.0065 
C) 0.0295 
D) 0.0395 
E) 0.0195 
A) 0.0095 
B) 0.0065 
C) 0.0295 
D) 0.0395 
E) 0.0195

Question 10

​Which of the following series is conditionally convergent? ​

Accepted Answer

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

Question 11

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

Accepted Answer

A) Ratio Test 
B) ρ-Series Test 
C) Alternating Series Test 
D) Telescoping Series Test 
E) Root Test 
A) Ratio Test 
B) ρ-Series Test 
C) Alternating Series Test 
D) Telescoping Series Test 
E) Root Test

Question 12

The Maclaurin series   represents which function below? ​

Accepted Answer

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

Question 13

Use the Limit Comparison Test to 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.

Question 14

Approximate the sum of the series by using the first six terms.

Accepted Answer

A) 1.799 < S < 1.805 
B) 1.794 < S < 1.806 
C) 1.794 < S < 1.805 
D) 1.792 < S < 1.792 
E) 1.698 < S < 1.902 
A) 1.799 < S < 1.805 
B) 1.794 < S < 1.806 
C) 1.794 < S < 1.805 
D) 1.792 < S < 1.792 
E) 1.698 < S < 1.902

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Write an equivalent series of the series   with the index of summation beginning at   . ​

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Identify the interval of convergence of a power series   . ​

Accepted Answer

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

Question 20

Find the sum of the convergent series. ​   ​

Accepted Answer

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

Write the first five terms of the sequence of partial sums.

Identify the interval of convergence of a power series .

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

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001.

True or false: The series converges.

Find a power series for the function centered at 0.

If ,the first three terms of the Taylor series expansion about for are

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

Consider the series .The sum of the series is Find the sum of the series .

Which of the following series is conditionally convergent?

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

The Maclaurin series represents which function below?

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

Approximate the sum of the series by using the first six terms.

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

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

Write an equivalent series of the series with the index of summation beginning at .

Find the Maclaurin polynomial of degree 4 for the function.

Identify the interval of convergence of a power series .

Find the sum of the convergent 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

Write the first five terms of the sequence of partial sums. ​ ​

Identify the interval of convergence of a power series . ​

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

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001. ​

True or false: The series converges. ​

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

If ​,the first three terms of the Taylor series expansion about for are ​

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

Consider the series .The sum of the series is Find the sum of the series . ​

​Which of the following series is conditionally convergent? ​

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

The Maclaurin series represents which function below? ​

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

Approximate the sum of the series by using the first six terms.

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

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

Write an equivalent series of the series with the index of summation beginning at . ​

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

Identify the interval of convergence of a power series . ​

Find the sum of the convergent 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

Write the first five terms of the sequence of partial sums.

Identify the interval of convergence of a power series .

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

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001.

True or false: The series converges.

Find a power series for the function centered at 0.

If ,the first three terms of the Taylor series expansion about for are

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

Consider the series .The sum of the series is Find the sum of the series .

Which of the following series is conditionally convergent?

The Maclaurin series represents which function below?

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

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

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

Write an equivalent series of the series with the index of summation beginning at .

Find the Maclaurin polynomial of degree 4 for the function.

Identify the interval of convergence of a power series .

Find the sum of the convergent series.