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)

Question 2

Write the repeating decimal   as a geometric series. ​

Accepted Answer

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

Question 3

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   ​ 
C)    secant line to   
D)    secant line to   
E)    tangent line to   
A)    tangent line to   at
  
B)    secant line to   ​ 
C)    secant line to   
D)    secant line to   
E)    tangent line to

Question 4

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 5

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

Accepted Answer

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

Question 6

Find the radius of convergence of the power series. ​   ​

Accepted Answer

A)    
B)    
C) 8 
D) ∞ 
E) 64 
A)    
B)    
C) 8 
D) ∞ 
E) 64

Question 7

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 8

Find the sum of the convergent series. ​   ​

Accepted Answer

A) 3 
B) 27 
C) 9 
D) 18 
E) 36 
A) 3 
B) 27 
C) 9 
D) 18 
E) 36

Question 9

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 10

Determine the convergence or divergence of the series. ​   ​

Accepted Answer

A) cannot be determined from the methods in the chapter 
B) Diverges 
C) Converges 
A) cannot be determined from the methods in the chapter 
B) Diverges 
C) Converges

Question 11

True or false: The series   diverges.
​

Accepted Answer

A) True 
 B)False

Question 12

Find the sum of the convergent series. ​   ​

Accepted Answer

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

Question 13

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Write an expression for the amount budgeted for this program after n years. ​

Accepted Answer

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

Question 14

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 15

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 16

Find the sum of the convergent series   ​

Accepted Answer

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

Question 17

Suppose a ball is dropped from a height of 16 feet.Each time it drops h feet,it rebounds 0.86h feet.Find the total distance traveled by the ball.Round your answer to two decimal places.

Accepted Answer

A) 244.57 feet 
B) 441.14 feet 
C) 196.57 feet 
D) 212.57 feet 
E) 228.57 feet 
A) 244.57 feet 
B) 441.14 feet 
C) 196.57 feet 
D) 212.57 feet 
E) 228.57 feet

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Use the Direct 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.

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

Write the repeating decimal as a geometric series.

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

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

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

Find the radius of convergence of the power series.

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

Find the sum of the convergent series.

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.

True or false: The series diverges.

Find the sum of the convergent series.

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Write an expression for the amount budgeted for this program after n years.

Determine the convergence or divergence of the series.

Determine the convergence or divergence of the series.

Find the sum of the convergent series

Suppose a ball is dropped from a height of 16 feet.Each time it drops h feet,it rebounds 0.86h feet.Find the total distance traveled by the ball.Round your answer to two decimal places.

Write an expression for the nth term of the sequence .

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

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

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. ) ​

Write the repeating decimal as a geometric series. ​

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

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

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

Find the radius of convergence of the power series. ​ ​

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

Find the sum of the convergent series. ​ ​

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. ​ ​

True or false: The series diverges. ​

Find the sum of the convergent series. ​ ​

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Write an expression for the amount budgeted for this program after n years. ​

Determine the convergence or divergence of the series. ​ ​

Determine the convergence or divergence of the series. ​ ​

Find the sum of the convergent series ​

Suppose a ball is dropped from a height of 16 feet.Each time it drops h feet,it rebounds 0.86h feet.Find the total distance traveled by the ball.Round your answer to two decimal places.

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

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

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

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

Write the repeating decimal as a geometric series.

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

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

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

Find the radius of convergence of the power series.

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

Find the sum of the convergent series.

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.

True or false: The series diverges.

Find the sum of the convergent series.

A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year.Write an expression for the amount budgeted for this program after n years.

Determine the convergence or divergence of the series.

Determine the convergence or divergence of the series.

Find the sum of the convergent series

Write an expression for the nth term of the sequence .

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

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