Question 1

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)    E

Question 2

Graph the sequence   .

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Match the sequence with its graph.

Accepted Answer

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

Question 5

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 6

Determine the convergence or divergence of the series.

Accepted Answer

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

Question 7

is the series   converges.

Accepted Answer

A) True 
 B)False

Question 8

Find a power series for the function   centered at 0.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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 11

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 12

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.

Accepted Answer

A)  4 
B)  2 
C)  5 
D)  7 
E)  3 
A)  4 
B)  2 
C)  5 
D)  7 
E)  3

Question 13

Find the fourth degree Taylor polynomial centered at   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

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 16

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

Accepted Answer

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

Question 17

Find all values of x for which the series   converges.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Find the Maclaurin polynomial of degree 3 for the function. ​   ​

Accepted Answer

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

Question 20

Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 7,000 units. Each year 25% of the units that have been sold will become inoperative. So, 7,000 units will be in use after 1 year,   units will be in use after 2 years, and so on. How many units will be in use after n years? ​

Accepted Answer

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

Find the interval of convergence of the power series . (Be sure to include a check for convergence at the endpoints of the interval.)

Graph the sequence .

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

Match the sequence with its graph.

Find the interval of convergence of the power series . (Be sure to include a check for convergence at the endpoints of the interval.)

Determine the convergence or divergence of the series.

is the series converges.

Find a power series for the function centered at 0.

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

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.

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

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

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

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

Find all values of x for which the series converges.

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

Find the Maclaurin polynomial of degree 3 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

Find the interval of convergence of the power series . (Be sure to include a check for convergence at the endpoints of the interval.)

Graph the sequence .

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

Match the sequence with its graph.

Find the interval of convergence of the power series . (Be sure to include a check for convergence at the endpoints of the interval.)

Determine the convergence or divergence of the series.

is the series converges.

Find a power series for the function centered at 0.

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

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ​ ​

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.005.

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

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

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

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

Find all values of x for which the series converges.

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

Find the Maclaurin polynomial of degree 3 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

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

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

Find the Maclaurin polynomial of degree 3 for the function.