Question 1

Determine whether the series   converges absolutely,converges conditionally,or diverges. ​

Accepted Answer

A) converges absolutely 
B) diverges 
C) converges conditionally 
A) converges absolutely 
B) diverges 
C) converges conditionally

Question 2

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.   ​

Accepted Answer

A) 11 
B) 6 
C) 9 
D) 7 
E) 5 
A) 11 
B) 6 
C) 9 
D) 7 
E) 5

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;Ratio Test 
B) converges;both p-series and Integral Test 
C) converges;p-series 
D) converges;Integral Test 
E) diverges;p-series 
A) diverges;Ratio Test 
B) converges;both p-series and Integral Test 
C) converges;p-series 
D) converges;Integral Test 
E) diverges;p-series

Question 4

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

Accepted Answer

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

Question 5

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 6

The Maclaurin series   represents which expression below?​ ​

Accepted Answer

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

Question 7

For function   ​ Using the Taylor series expansion for   about   ,the second degree estimate for   is ​

Accepted Answer

A) ​4.335 
B) ​4.750 
C) ​4.420 
D) ​5.240 
A) ​4.335 
B) ​4.750 
C) ​4.420 
D) ​5.240

Question 8

Write the first three terms of the sequence. ​   ​

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

If the rate of inflation is   per year and the average price of a car is currently $40,000,the average price after n years is   .Compute the average price after 4 years.Round your answer to two decimal places. ​

Accepted Answer

A) $30,570.77 
B) $51,458.65 
C) $170,400.00 
D) $47,397.16 
E) $149,600.00 
A) $30,570.77 
B) $51,458.65 
C) $170,400.00 
D) $47,397.16 
E) $149,600.00

Question 12

Find the third Taylor polynomial for   expanded about   . ​

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A) converges for   
B) diverges only at   
C) converges for   
D) converges for   
E) converges for   
A) converges for   
B) diverges only at   
C) converges for   
D) converges for   
E) converges for

Question 15

True or false: The series   converges.
​

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

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

Question 17

Find the fourth degree Maclaurin polynomial for the function. ​   ​

Accepted Answer

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

Question 18

Determine whether the series   converges conditionally or absolutely,or diverges. ​

Accepted Answer

A) The series converges absolutely. 
B) The series diverges. 
C) The series converges absolutely but does not converge conditionally. 
D) The series converges conditionally but does not converge absolutely. 
A) The series converges absolutely. 
B) The series diverges. 
C) The series converges absolutely but does not converge conditionally. 
D) The series converges conditionally but does not converge absolutely.

Question 19

Use the binomial series to find the Maclaurian series for the function   . ​

Accepted Answer

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

Determine whether the series converges absolutely,converges conditionally,or diverges.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.

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

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

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

The Maclaurin series represents which expression below?

For function Using the Taylor series expansion for about ,the second degree estimate for is

Write the first three terms of the sequence.

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

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

If the rate of inflation is per year and the average price of a car is currently $40,000,the average price after n years is .Compute the average price after 4 years.Round your answer to two decimal places.

Find the third Taylor polynomial for expanded about .

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

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

True or false: The series converges.

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

Find the fourth degree Maclaurin polynomial for the function.

Determine whether the series converges conditionally or absolutely,or diverges.

Use the binomial series to find the Maclaurian series 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

Determine whether the series converges absolutely,converges conditionally,or diverges. ​

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001. ​

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

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

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

The Maclaurin series represents which expression below?​ ​

For function ​ Using the Taylor series expansion for about ,the second degree estimate for is ​

Write the first three terms of the sequence. ​ ​

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

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

If the rate of inflation is per year and the average price of a car is currently $40,000,the average price after n years is .Compute the average price after 4 years.Round your answer to two decimal places. ​

Find the third Taylor polynomial for expanded about . ​

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

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

True or false: The series converges. ​

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

Find the fourth degree Maclaurin polynomial for the function. ​ ​

Determine whether the series converges conditionally or absolutely,or diverges. ​

Use the binomial series to find the Maclaurian series 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

Determine whether the series converges absolutely,converges conditionally,or diverges.

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.

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

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

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

The Maclaurin series represents which expression below?

For function Using the Taylor series expansion for about ,the second degree estimate for is

Write the first three terms of the sequence.

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

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

If the rate of inflation is per year and the average price of a car is currently $40,000,the average price after n years is .Compute the average price after 4 years.Round your answer to two decimal places.

Find the third Taylor polynomial for expanded about .

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

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

True or false: The series converges.

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

Find the fourth degree Maclaurin polynomial for the function.

Determine whether the series converges conditionally or absolutely,or diverges.

Use the binomial series to find the Maclaurian series for the function .