Question 1

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 2

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 3

Use the power series   to determine a power series for the function   .

Accepted Answer

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

Question 4

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 5

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

Accepted Answer

A)  The series converges absolutely. 
B)  The series diverges. 
C)  The series converges absolutely but does not converge conditionally. 
D)  The series converges conditionally but does not converge absolutely. 
A)  The series converges absolutely. 
B)  The series diverges. 
C)  The series converges absolutely but does not converge conditionally. 
D)  The series converges conditionally but does not converge absolutely.

Question 6

is the series   diverges.

Accepted Answer

A) True 
 B)False

Question 7

Find the Maclaurin polynomial of degree two for the function   .

Accepted Answer

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

Question 8

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 9

A government program that currently costs taxpayers $4.5 billion per year is cut back by 20 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 10

Find the Maclaurin polynomial of degree 4 for the function.

Accepted Answer

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

Question 11

is the series   diverges .

Accepted Answer

A) True 
 B)False

Question 12

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of   at   .

Accepted Answer

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

Question 13

Write an equivalent series of the series   with the index of summation beginning at   .

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

is the series   converges.

Accepted Answer

A) True 
 B)False

Question 16

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 17

Write an expression for the nth term of the sequence   .

Accepted Answer

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

Question 18

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   
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 19

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

Accepted Answer

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

Question 20

Write the first five terms of the sequence.

Accepted Answer

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

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

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

Use the power series to determine a power series for the function .

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

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

is the series diverges.

Find the Maclaurin polynomial of degree two for the function .

Determine the convergence or divergence of the series.

A government program that currently costs taxpayers $4.5 billion per year is cut back by 20 percent per year. Write an expression for the amount budgeted for this program after n years.

Find the Maclaurin polynomial of degree 4 for the function.

is the series diverges .

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of at .

Write an equivalent series of the series with the index of summation beginning at .

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

is the series converges.

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

Write an expression for the nth term of the sequence .

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 Root Test to determine the convergence or divergence of the series.

Write the first five terms of the sequence.

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

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

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

Use the power series to determine a power series for the function .

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

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

is the series diverges.

Find the Maclaurin polynomial of degree two for the function .

Determine the convergence or divergence of the series.

A government program that currently costs taxpayers $4.5 billion per year is cut back by 20 percent per year. Write an expression for the amount budgeted for this program after n years. ​

Find the Maclaurin polynomial of degree 4 for the function.

is the series diverges .

Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of at .

Write an equivalent series of the series with the index of summation beginning at .

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

is the series converges.

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

Write an expression for the nth term of the sequence .

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 Root Test to determine the convergence or divergence of the series.

Write the first five terms of the sequence.

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

A government program that currently costs taxpayers $4.5 billion per year is cut back by 20 percent per year. Write an expression for the amount budgeted for this program after n years.

Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of at .

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