Question 1

Determine the convergence or divergence of the series.

Accepted Answer

A)  diverges 
B)  converges 
C)  cannot be determined 
A)  diverges 
B)  converges 
C)  cannot be determined

Question 2

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 3

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

Accepted Answer

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

Question 4

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year. Compute the budget after the fourth year. Round your answer to the nearest integer.

Accepted Answer

A)  $1,433,600,000 
B)  $165,995,062 
C)  $89,600,000 
D)  $1,012,217,284 
E)  $453,600,000 
A)  $1,433,600,000 
B)  $165,995,062 
C)  $89,600,000 
D)  $1,012,217,284 
E)  $453,600,000

Question 5

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 6

Identify the most appropriate test to be used to determine whether the series   converges or diverges.

Accepted Answer

A)  Limit Comparison Test with   
B)  Direct Comparison Test with   
C)  Alternating Series Test 
D)  Root Test 
E)  Ratio Test 
A)  Limit Comparison Test with   
B)  Direct Comparison Test with   
C)  Alternating Series Test 
D)  Root Test 
E)  Ratio Test

Question 7

Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

Accepted Answer

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

Question 8

Find the Maclaurin polynomial of degree 5 for the function.

Accepted Answer

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

Question 9

Use the Limit 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 10

Write the first three terms of the sequence.

Accepted Answer

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

Question 11

The terms of a series   are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning.   ,

Accepted Answer

A)  diverges; Ratio Test 
B)  converges; Ratio Test 
C)  converges; Integral Test 
D)  diverges; Alternating Series Test 
E)  diverges; Root Test 
A)  diverges; Ratio Test 
B)  converges; Ratio Test 
C)  converges; Integral Test 
D)  diverges; Alternating Series Test 
E)  diverges; Root Test

Question 12

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

Accepted Answer

A)  converges 
B)  diverges 
C)  Limit Comparison Test does not apply 
A)  converges 
B)  diverges 
C)  Limit Comparison Test does not apply

Question 13

Find the Maclaurin series for the function   .

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Write an expression for the nth term of the sequence   .

Accepted Answer

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

Question 16

Use the series   for   to approximate the value of   using   . Round your answer to three decimal places.

Accepted Answer

A)  0.091 
B)  0.083 
C)  0.100 
D)  0.077 
E)  0.095 
A)  0.091 
B)  0.083 
C)  0.100 
D)  0.077 
E)  0.095

Question 17

is the series   is convergent.

Accepted Answer

A) True 
 B)False

Question 18

Find a power series for the function   centered at 1.

Accepted Answer

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

Question 19

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

Accepted Answer

A)  The series converges for   . 
B)  The series converges for   . 
C)  The series diverges for all positive values of p. 
D)  The series converges for   . 
E)  The series converges for   . 
A)  The series converges for   . 
B)  The series converges for   . 
C)  The series diverges for all positive values of p. 
D)  The series converges for   . 
E)  The series converges for   .

Question 20

Find the Maclaurin polynomial of degree 4 for the function. ​   ​

Accepted Answer

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

Determine the convergence or divergence of the series.

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

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

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year. Compute the budget after the fourth year. Round your answer to the nearest integer.

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

Identify the most appropriate test to be used to determine whether the series converges or diverges.

Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

Find the Maclaurin polynomial of degree 5 for the function.

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

Write the first three terms of the sequence.

The terms of a series are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. ,

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

Find the Maclaurin series for the function .

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

Write an expression for the nth term of the sequence .

Use the series for to approximate the value of using . Round your answer to three decimal places.

is the series is convergent.

Find a power series for the function centered at 1.

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

Find the Maclaurin polynomial of degree 4 for the function.

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

Determine the convergence or divergence of the series.

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

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

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year. Compute the budget after the fourth year. Round your answer to the nearest integer.

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

Identify the most appropriate test to be used to determine whether the series converges or diverges.

Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

Find the Maclaurin polynomial of degree 5 for the function.

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

Write the first three terms of the sequence.

The terms of a series are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. ,

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

Find the Maclaurin series for the function .

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

Write an expression for the nth term of the sequence .

Use the series for to approximate the value of using . Round your answer to three decimal places.

is the series is convergent.

Find a power series for the function centered at 1.

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

Find the Maclaurin polynomial of degree 4 for the function. ​ ​

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 .

Find the Maclaurin polynomial of degree 4 for the function.