Question 1

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

Accepted Answer

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

Question 2

What is   a first-degree polynomial function whose value and slope agree with the value and slope of   at   ?

Accepted Answer

A)    is the tangent line to the curve   at the point   . 
B)    is the tangent line to the curve   at the point   
C)    is the tangent line to the curve   at the point   
D)    is the tangent line to the curve   at the point   
E)    is the tangent line to the curve   at the point   
A)    is the tangent line to the curve   at the point   . 
B)    is the tangent line to the curve   at the point   
C)    is the tangent line to the curve   at the point   
D)    is the tangent line to the curve   at the point   
E)    is the tangent line to the curve   at the point

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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 8

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

Accepted Answer

A)  diverges; both Ratio Test and Theorem 9.9 (nth Term Test for Divergence) 
B)  converges; Integral Test 
C)  diverges; Theorem 9.9 (nth Term Test for Divergence) 
D)  converges; p-series 
E)  diverges; Ratio Test 
A)  diverges; both Ratio Test and Theorem 9.9 (nth Term Test for Divergence) 
B)  converges; Integral Test 
C)  diverges; Theorem 9.9 (nth Term Test for Divergence) 
D)  converges; p-series 
E)  diverges; Ratio Test

Question 9

Find the fourth degree Maclaurin polynomial for the function. ​   ​

Accepted Answer

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

Question 10

Approximate the sum of the series by using the first six terms.

Accepted Answer

A)  0.723 < S < 0.743 
B)  0.683 < S < 0.763 
C)  0.733 < S < 0.738 
D)  0.693 < S < 0.733 
E)  0.73 < S < 0.736 
A)  0.723 < S < 0.743 
B)  0.683 < S < 0.763 
C)  0.733 < S < 0.738 
D)  0.693 < S < 0.733 
E)  0.73 < S < 0.736

Question 11

Find the sum of the convergent series   by using a well-known function. Round your answer to four decimal places.

Accepted Answer

A)  0.0713 
B)  0.0907 
C)  0.8288 
D)  0.0768 
E)  0.0831 
A)  0.0713 
B)  0.0907 
C)  0.8288 
D)  0.0768 
E)  0.0831

Question 12

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function   to be less than 0.001. ​

Accepted Answer

A)    
B)  1 
C)  2 
D)  7 
E)  3 
A)    
B)  1 
C)  2 
D)  7 
E)  3

Question 13

is the series   is convergent.

Accepted Answer

A) True 
 B)False

Question 14

Match the sequence with its graph.

Accepted Answer

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

Question 15

Identify the interval of convergence of a power series   .

Accepted Answer

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

Question 16

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.

Accepted Answer

A)  11 
B)  6 
C)  9 
D)  7 
E)  5 
A)  11 
B)  6 
C)  9 
D)  7 
E)  5

Question 17

Use the polynomial test to determine whether the series   converges or diverges.

Accepted Answer

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

Question 18

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 19

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.

Question 20

is the series   converges.

Accepted Answer

A) True 
 B)False

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

What is a first-degree polynomial function whose value and slope agree with the value and slope of at ?

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

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

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

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

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 the fourth degree Maclaurin polynomial for the function.

Approximate the sum of the series by using the first six terms.

Find the sum of the convergent series by using a well-known function. Round your answer to four decimal places.

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001.

is the series is convergent.

Match the sequence with its graph.

Identify the interval of convergence of a power series .

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.

Use the polynomial test to determine whether the series converges or diverges.

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

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

is the series converges.

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

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

What is a first-degree polynomial function whose value and slope agree with the value and slope of at ?

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

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

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

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

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 the fourth degree Maclaurin polynomial for the function. ​ ​

Approximate the sum of the series by using the first six terms.

Find the sum of the convergent series by using a well-known function. Round your answer to four decimal places.

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001. ​

is the series is convergent.

Match the sequence with its graph.

Identify the interval of convergence of a power series .

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.001.

Use the polynomial test to determine whether the series converges or diverges.

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

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

is the series converges.

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

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

Find the fourth degree Maclaurin polynomial for the function.

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function to be less than 0.001.