Question 1

Find the differential equation having the solution   . ​

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find a power series for the function   centered at 0.

Accepted Answer

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

Question 4

Sketch the graph of the sequence of partial sum of the series   . ​

Accepted Answer

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

Question 5

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

Accepted Answer

A)  diverges 
B)  converges 
C)  Theorem 9.11 inconclusive 
A)  diverges 
B)  converges 
C)  Theorem 9.11 inconclusive

Question 6

Evaluate   using the formula   where k is a real number, n is a positive integer, and   .

Accepted Answer

A)  80 
B)  66 
C)  126 
D)  70 
E)  56 
A)  80 
B)  66 
C)  126 
D)  70 
E)  56

Question 7

Use a graphing utility to graph   and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at   . ​

Accepted Answer

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

Question 8

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

Accepted Answer

A)  Ratio Test 
B)  ρ-Series Test 
C)  Alternating Series Test 
D)  Telescoping Series Test 
E)  Root Test 
A)  Ratio Test 
B)  ρ-Series Test 
C)  Alternating Series Test 
D)  Telescoping Series Test 
E)  Root Test

Question 9

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

Accepted Answer

A)  The sequence converges to 0. 
B)  The sequence diverges to -2. 
C)  The sequence converges to 1. 
D)  The sequence converges to -1. 
E)  The sequence diverges. 
A)  The sequence converges to 0. 
B)  The sequence diverges to -2. 
C)  The sequence converges to 1. 
D)  The sequence converges to -1. 
E)  The sequence diverges.

Question 10

Use the Limit 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 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

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 13

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

Accepted Answer

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

Question 14

A deposit of $250 is made at the beginning of each month into an account at an annual interest rate of 3% compounded monthly. The balance in the account after n months is   . Find the balance in the account after 3 years by computing the 36th term of the sequence. Round your answer to two decimal places. ​

Accepted Answer

A)  $9,428.65 
B)  $753.76 
C)  $7,551.03 
D)  $19,717.22 
E)  $1,511.28 
A)  $9,428.65 
B)  $753.76 
C)  $7,551.03 
D)  $19,717.22 
E)  $1,511.28

Question 15

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 16

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

Accepted Answer

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

Question 17

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 18

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)    
A)    
B)    
C)    
D)    
E)

Question 19

Find the Maclaurian series for the function   . ​

Accepted Answer

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

Question 20

Consider the function   and its second-degree polynomial   at   Compute the value of   and   Round your answer to four decimal places.

Accepted Answer

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

Find the differential equation having the solution .

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

Find a power series for the function centered at 0.

Sketch the graph of the sequence of partial sum of the series .

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

Evaluate using the formula where k is a real number, n is a positive integer, and .

Use a graphing utility to graph and P₁, a first-degree polynomial function whose value and slope agree with the value and slope of f at .

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

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

Use the Limit 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.)

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

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

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

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

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

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

Find the Maclaurian series for the function .

Consider the function and its second-degree polynomial at Compute the value of and Round your answer to four 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 differential equation having the solution . ​

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

Find a power series for the function centered at 0.

Sketch the graph of the sequence of partial sum of the series . ​

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

Evaluate using the formula where k is a real number, n is a positive integer, and .

Use a graphing utility to graph and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at . ​

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

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

Use the Limit 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.)

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

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

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

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

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

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

Find the Maclaurian series for the function . ​

Consider the function and its second-degree polynomial at Compute the value of and Round your answer to four 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

Find the differential equation having the solution .

Sketch the graph of the sequence of partial sum of the series .

Use a graphing utility to graph and P₁, a first-degree polynomial function whose value and slope agree with the value and slope of f at .

Find the Maclaurian series for the function .