Question 1

True or false.The series  is divergent.
​

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

A) converges 
B) Ratio Test inconclusive 
C) diverges

Question 3

True or false.The series  is convergent.
​

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Let  be the Taylor expansion for​  about  .Find the general term for  and find  .

Accepted Answer

The answer of Let  be the Taylor expansion for​...

Question 7

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

Accepted Answer

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

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)

Question 9

Identify the graph of the first 10 terms of the sequence of partial sum of the series  for  . ​

Accepted Answer

A) ​
 
B) ​
 
C) ​
 
D) ​
 
E) ​

Question 10

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

Accepted Answer

A) Ratio Test inconclusive 
B) converges 
C) diverges

Question 11

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at  .What is P1 called? ​  ​

Accepted Answer

A)   ;tangent line to  at
 
B)   ;secant line to  at
 
C)   ;tangent line to  at
 
D)   ;differential of  at
 
E)   ;tangent line to  at

Question 13

Find a power series for the function  centered at 1. ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Suppose the winner of a $15,000,000 sweepstakes will be paid $500,000 per year for 30 years,starting a year from now.The money earns 5% interest per year.The present value of the winnings is  Compute the present value using the formula for the nth partial sum of a geometric series.Round your answer to two decimal places. ​

Accepted Answer

A) $36,941,323.46 
B) $9,464,644.76 
C) $24,627,548.97 
D) $5,189,829.02 
E) $7,686,225.51

Question 15

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

Accepted Answer

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

Question 16

Let  be a function that is differentiable for all  .The Taylor expansion for  about  is given by  The first four nonzero terms of  are given by 
-Show that  converges for all  .​​

Accepted Answer

The answer of Let  be a function that is...

Question 17

The sixth degree term of the Taylor series expansion for  about  has coefficient​ ​

Accepted Answer

A) ​  
B) ​  
C) ​  
D) ​

Question 18

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

Accepted Answer

A) diverges 
B) converges 
C) Theorem 9.11 inconclusive

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

Exam 9: Infinite Series

True or false.The series is divergent.

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

True or false.The series is convergent.

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

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

Let be the Taylor expansion for about .Find the general term for and find .

Use the definition to find the Taylor series centered at 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. )

Identify the graph of the first 10 terms of the sequence of partial sum of the series for .

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

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

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at .What is P₁ called?

Find a power series for the function centered at 1.

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

Let be a function that is differentiable for all .The Taylor expansion for about is given by The first four nonzero terms of are given by -Show that converges for all .

The sixth degree term of the Taylor series expansion for about has coefficient

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

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

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

Exam 9: Infinite Series

True or false.The series is divergent. ​

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

True or false.The series is convergent. ​

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

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

Let be the Taylor expansion for​ about .Find the general term for and find .

Use the definition to find the Taylor series centered at 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. ) ​ ​

Identify the graph of the first 10 terms of the sequence of partial sum of the series for . ​

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

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

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at .What is P1 called? ​ ​

Find a power series for the function centered at 1. ​

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

Let be a function that is differentiable for all .The Taylor expansion for about is given by The first four nonzero terms of are given by -Show that converges for all .​​

The sixth degree term of the Taylor series expansion for about has coefficient​ ​

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

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

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

True or false.The series is divergent.

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

True or false.The series is convergent.

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

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

Let be the Taylor expansion for about .Find the general term for and find .

Use the definition to find the Taylor series centered at 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. )

Identify the graph of the first 10 terms of the sequence of partial sum of the series for .

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

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

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of f at .What is P₁ called?

Find a power series for the function centered at 1.

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

Let be a function that is differentiable for all .The Taylor expansion for about is given by The first four nonzero terms of are given by -Show that converges for all .

The sixth degree term of the Taylor series expansion for about has coefficient

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

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

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