Question 1

Find the values of x for which the series   converges.

Accepted Answer

A)  -   <   < 0 
B)  0 <   <   
C)  -   <   <   
D)  -   <   <   
E)  0 <   <   
A)  -   <   < 0 
B)  0 <   <   
C)  -   <   <   
D)  -   <   <   
E)  0 <   <

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A)  0.0037 
B)  0.0007 
C)  0.0237 
D)  0.0337 
E)  0.0137 
A)  0.0037 
B)  0.0007 
C)  0.0237 
D)  0.0337 
E)  0.0137

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Suppose the annual spending by tourists in a resort city is $100 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)  $800 million 
B)  $401 million 
C)  $200 million 
D)  $801 million 
E)  $400 million 
A)  $800 million 
B)  $401 million 
C)  $200 million 
D)  $801 million 
E)  $400 million

Question 8

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 9

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 10

Identify the interval of convergence of a power series   .

Accepted Answer

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

Question 11

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 12

Consider the sequence   whose nth term is given by   where P is the principal,   is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if   and   . Round your answer to two decimal places. ​

Accepted Answer

A)  $9,518.26 
B)  $10,061.16 
C)  $9,696.45 
D)  $9,342.82 
E)  $9,412.67 
A)  $9,518.26 
B)  $10,061.16 
C)  $9,696.45 
D)  $9,342.82 
E)  $9,412.67

Question 13

Identify the interval of convergence of a power series   .

Accepted Answer

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

Question 14

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 15

is the infinite series   .

Accepted Answer

A) True 
 B)False

Question 16

Find the third degree Taylor polynomial centered at   for the function. ​   ​

Accepted Answer

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

Question 17

is the series   converges.

Accepted Answer

A) True 
 B)False

Question 18

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 19

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

Accepted Answer

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

Question 20

If the rate of inflation is   per year and the average price of a car is currently $35,000, the average price after n years is   . Compute the average price after 8 years. Round your answer to two decimal places.

Accepted Answer

A)  $22,259.86 
B)  $53,714.03 
C)  $295,400.00 
D)  $46,685.40 
E)  $264,600.00 
A)  $22,259.86 
B)  $53,714.03 
C)  $295,400.00 
D)  $46,685.40 
E)  $264,600.00

Find the values of x for which the series converges.

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

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

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

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

Use the binomial series to 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.)

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

Identify the interval of convergence of a power series .

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

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places.

Identify the interval of convergence of a power series .

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

is the infinite series .

Find the third degree Taylor polynomial centered at for the function.

is the series converges.

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

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 $35,000, the average price after n years is . Compute the average price after 8 years. Round your answer to two decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 9: Infinite Series

Find the values of x for which the series converges.

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

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

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

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

Use the binomial series to 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.)

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

Identify the interval of convergence of a power series .

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

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places. ​

Identify the interval of convergence of a power series .

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

is the infinite series .

Find the third degree Taylor polynomial centered at for the function. ​ ​

is the series converges.

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

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 $35,000, the average price after n years is . Compute the average price after 8 years. Round your answer to two decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

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

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

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

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places.

Find the third degree Taylor polynomial centered at for the function.