Question 1

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

Accepted Answer

A) 1.457 < S < 1.477 
B) 1.417 < S < 1.497 
C) 1.467 < S < 1.472 
D) 1.427 < S < 1.467 
E) 1.461 < S < 1.473 
A) 1.457 < S < 1.477 
B) 1.417 < S < 1.497 
C) 1.467 < S < 1.472 
D) 1.427 < S < 1.467 
E) 1.461 < S < 1.473

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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 5

Write the first five terms of the sequence. ​   ​

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Find the Maclaurian series for the function   . ​

Accepted Answer

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

Question 10

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 11

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.   ​

Accepted Answer

A) 6 
B) 4 
C) 5 
D) 8 
E) 3 
A) 6 
B) 4 
C) 5 
D) 8 
E) 3

Question 12

Which of the following series diverge?   ​ ​

Accepted Answer

A) ​I only 
B) ​II only 
C) ​I and II only 
D) ​I and III only 
A) ​I only 
B) ​II only 
C) ​I and II only 
D) ​I and III only

Question 13

Find the Maclaurin polynomial of degree 3 for the function. ​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Use the Direct 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 16

Find the Maclaurin series for the function   . ​

Accepted Answer

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

Question 17

Use Theorem 9.11 to determine the convergence or divergence of the series. ​   ​

Accepted Answer

A) converges 
B) diverges 
C) Theorem 9.11 inconclusive 
A) converges 
B) diverges 
C) Theorem 9.11 inconclusive

Question 18

​Let   represent the Taylor Polynomial of degree n about   for   .If   is used to approximate the value of   ,then which of the following expressions is NOT less than   ? ​

Accepted Answer

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

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 diverges. 
B) The sequence converges to 2. 
C) The sequence converges to -1. 
D) The sequence converges to 1. 
E) The sequence converges to 0. 
A) The sequence diverges. 
B) The sequence converges to 2. 
C) The sequence converges to -1. 
D) The sequence converges to 1. 
E) The sequence converges to 0.

Question 20

​The power series   converges for which values of x? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​​   is any real number. 
A) ​   
B) ​   
C) ​   
D) ​​   is any real number.

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

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

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

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

Write the first five terms of the sequence.

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

Find a power series for the function centered at 0.

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

Find the Maclaurian series for the function .

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

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.

Which of the following series diverge?

Find the Maclaurin polynomial of degree 3 for the function.

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

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

Find the Maclaurin series for the function .

Use Theorem 9.11 to determine the convergence or divergence of the series.

Let represent the Taylor Polynomial of degree n about for .If is used to approximate the value of ,then which of the following expressions is NOT less than ?

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

The power series converges for which values of x?

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

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

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

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

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

Write the first five terms of the sequence. ​ ​

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

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

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

Find the Maclaurian series for the function . ​

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

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008. ​

Which of the following series diverge? ​ ​

Find the Maclaurin polynomial of degree 3 for the function. ​ ​

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

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

Find the Maclaurin series for the function . ​

Use Theorem 9.11 to determine the convergence or divergence of the series. ​ ​

​Let represent the Taylor Polynomial of degree n about for .If is used to approximate the value of ,then which of the following expressions is NOT less than ? ​

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

​The power series converges for which values of x? ​

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

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

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

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

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

Write the first five terms of the sequence.

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

Find a power series for the function centered at 0.

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

Find the Maclaurian series for the function .

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

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.008.

Which of the following series diverge?

Find the Maclaurin polynomial of degree 3 for the function.

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

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

Find the Maclaurin series for the function .

Use Theorem 9.11 to determine the convergence or divergence of the series.

Let represent the Taylor Polynomial of degree n about for .If is used to approximate the value of ,then which of the following expressions is NOT less than ?

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

The power series converges for which values of x?