Question 1

Find the next three terms of the geometric sequence 8,40,200,.... ​​

Accepted Answer

A)  ​232, 264, 296 
B)  ​1,000, 5,000, 25,000 
C)  ​360, 520, 680 
D)  ​205, 210, 215 
E)  200,1,000,5,000 
A)  ​232, 264, 296 
B)  ​1,000, 5,000, 25,000 
C)  ​360, 520, 680 
D)  ​205, 210, 215 
E)  200,1,000,5,000 B

Question 2

Find the radius of convergence of the series ​   ​

Accepted Answer

A)  ​16 
B)  ​18 
C)  ​1 
D)  ​9 
E)  ​8 
A)  ​16 
B)  ​18 
C)  ​1 
D)  ​9 
E)  ​8 E

Question 3

What are the next three terms in the arithmetic sequence -2,-6,-10,.... ​​

Accepted Answer

A)  ​-14, -18, -22 
B)  ​2, 6, 10 
C)  ​56, -224, 896 
D)  ​-8, -10, -12 
E)  -10,-14,-18 
A)  ​-14, -18, -22 
B)  ​2, 6, 10 
C)  ​56, -224, 896 
D)  ​-8, -10, -12 
E)  -10,-14,-18 A

Question 4

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​   ​   ​

Accepted Answer

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

Question 5

Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​

Accepted Answer

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

Question 6

The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars)and find the sum of the series.

Accepted Answer

A)  The geometric series is   The sum of the series is $3600 million. 
B)  The geometric series is   The sum of the series is $67,500 million. 
C)  The geometric series is   The sum of the series is 3600 million. 
D)  The geometric series is   The sum of the series is $67,500 million. 
E)  The geometric series is   The sum of the series is $675 million. 
A)  The geometric series is   The sum of the series is $3600 million. 
B)  The geometric series is   The sum of the series is $67,500 million. 
C)  The geometric series is   The sum of the series is 3600 million. 
D)  The geometric series is   The sum of the series is $67,500 million. 
E)  The geometric series is   The sum of the series is $675 million.

Question 7

​Find the power series for the function   using the power series for   ​

Accepted Answer

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

Question 8

​Find the radius of convergence centered at   for the following function. ​   ​

Accepted Answer

A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​   
A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​

Question 9

Use the Ratio 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 10

Write an expression for the ​nth term of the sequence   ,   ,   ,   ,.... ​​

Accepted Answer

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

Question 11

​Use the sixth-degree Taylor polynomial centered at   for the function   to approximate   Round your answer to nearest ten thousandth. ​

Accepted Answer

A)  ​0.2295 
B)  ​0.2197 
C)  ​0.2397 
D)  ​0.1185 
E)  ​0.1436 
A)  ​0.2295 
B)  ​0.2197 
C)  ​0.2397 
D)  ​0.1185 
E)  ​0.1436

Question 12

​​Determine the convergence or divergence of the following series. ​   ​

Accepted Answer

A)  ​inconclusive 
B)  ​converges 
C)  ​diverges 
A)  ​inconclusive 
B)  ​converges 
C)  ​diverges

Question 13

​Find the radius of convergence of the series   ​

Accepted Answer

A)  ​1 
B)  ​2 
C)  ​3 
D)  ​7 
E)  ​9 
A)  ​1 
B)  ​2 
C)  ​3 
D)  ​7 
E)  ​9

Question 14

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

Accepted Answer

A)  ​Diverges. 
B)  Converges. 
C)  ​Ratio Test is inconclusive. 
A)  ​Diverges. 
B)  Converges. 
C)  ​Ratio Test is inconclusive.

Question 15

Find the limit of the following sequence. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The limit does not exist. 
A)    
B)    
C)    
D)    
E)  The limit does not exist.

Question 16

Complete two iterations of Newton´s Method for the function   using the initial guess 2.9. ​ ​

Accepted Answer

A)  ​3.001834, 2.9998 
B)  ​3.001864, 3.0002 
C)  ​3.001864, 3.0001 
D)  ​3.001724, 3 
E)  ​3.001514,2.9999 
A)  ​3.001834, 2.9998 
B)  ​3.001864, 3.0002 
C)  ​3.001864, 3.0001 
D)  ​3.001724, 3 
E)  ​3.001514,2.9999

Question 17

​Find the radius of convergence centered at   for the following function. ​   ​

Accepted Answer

A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​   
A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​

Question 18

​Test the series   for convergence or divergence using any appropriate test. ​

Accepted Answer

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

Question 19

​Determine the convergence or divergence of the series   Use a symbolic algebra utility to verify your result. ​​

Accepted Answer

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

Question 20

​Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4. ​   ​

Accepted Answer

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

Find the next three terms of the geometric sequence 8,40,200,....

Find the radius of convergence of the series

What are the next three terms in the arithmetic sequence -2,-6,-10,....

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

Write an expression for the nth term of the sequence 4,24,124,624,....

Find the power series for the function using the power series for

Find the radius of convergence centered at for the following function.

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

Write an expression for the nth term of the sequence , , , ,....

Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth.

Determine the convergence or divergence of the following series.

Find the radius of convergence of the series

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

Find the limit of the following sequence.

Complete two iterations of Newton´s Method for the function using the initial guess 2.9.

Find the radius of convergence centered at for the following function.

Test the series for convergence or divergence using any appropriate test.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Exam 10: Series and Taylor Polynomials

Find the next three terms of the geometric sequence 8,40,200,.... ​​

Find the radius of convergence of the series ​ ​

What are the next three terms in the arithmetic sequence -2,-6,-10,.... ​​

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​

Write an expression for the ​nth term of the sequence 4,24,124,624,.... ​​

​Find the power series for the function using the power series for ​

​Find the radius of convergence centered at for the following function. ​ ​

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

Write an expression for the ​nth term of the sequence , , , ,.... ​​

​Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth. ​

​​Determine the convergence or divergence of the following series. ​ ​

​Find the radius of convergence of the series ​

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

Find the limit of the following sequence. ​ ​

Complete two iterations of Newton´s Method for the function using the initial guess 2.9. ​ ​

​Find the radius of convergence centered at for the following function. ​ ​

​Test the series for convergence or divergence using any appropriate test. ​

​Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result. ​​

​Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Find the next three terms of the geometric sequence 8,40,200,....

Find the radius of convergence of the series

What are the next three terms in the arithmetic sequence -2,-6,-10,....

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

Write an expression for the nth term of the sequence 4,24,124,624,....

Find the power series for the function using the power series for

Find the radius of convergence centered at for the following function.

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

Write an expression for the nth term of the sequence , , , ,....

Use the sixth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest ten thousandth.

Determine the convergence or divergence of the following series.

Find the radius of convergence of the series

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

Find the limit of the following sequence.

Complete two iterations of Newton´s Method for the function using the initial guess 2.9.

Find the radius of convergence centered at for the following function.

Test the series for convergence or divergence using any appropriate test.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.