Question 1

Use a power series to approximate the value of the integral   with an error less than 0.001. Round your answer to four decimal places.

Accepted Answer

A)  0.1063 
B)  0.0900 
C)  0.0982 
D)  0.1071 
E)  0.0985 
A)  0.1063 
B)  0.0900 
C)  0.0982 
D)  0.1071 
E)  0.0985

Question 2

Find the third Taylor polynomial for   expanded about   .

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Find the radius of convergence of the power series.

Accepted Answer

A)    
B)  14 
C)  49 
D)  0 
E)  7 
A)    
B)  14 
C)  49 
D)  0 
E)  7

Question 5

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 6

Write the repeating decimal   as a geometric series.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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 9

Write the next two apparent terms of the sequence   .

Accepted Answer

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

Question 10

Find a power series for the function   centered at 0.

Accepted Answer

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

Question 11

Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places. ​

Accepted Answer

A)  $5,368,709.12 
B)  $2,684,354.56 
C)  $10,737,418.22 
D)  $42,949,672.88 
E)  $21,474,836.44 
A)  $5,368,709.12 
B)  $2,684,354.56 
C)  $10,737,418.22 
D)  $42,949,672.88 
E)  $21,474,836.44

Question 12

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

Accepted Answer

A)  0.783 < S < 4.630 
B)  2.066 < S < 3.348 
C)  1.745 < S < 3.669 
D)  0.569 < S < 4.844 
E)  0.302 < S < 5.111 
A)  0.783 < S < 4.630 
B)  2.066 < S < 3.348 
C)  1.745 < S < 3.669 
D)  0.569 < S < 4.844 
E)  0.302 < S < 5.111

Question 13

is the series   diverges.

Accepted Answer

A) True 
 B)False

Question 14

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 15

Suppose the winner of a $10,000,000 sweepstakes will be paid $200,000 per year for 50 years, starting a year from now. The money earns 6% interest per year. The present value of the winnings is   Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.

Accepted Answer

A)  $10,542,883.62 
B)  $3,323,509.25 
C)  $7,028,589.08 
D)  $2,556,671.23 
E)  $3,152,372.13 
A)  $10,542,883.62 
B)  $3,323,509.25 
C)  $7,028,589.08 
D)  $2,556,671.23 
E)  $3,152,372.13

Question 16

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 17

Use the Limit Comparison Test (if possible) to determine whether the series   converges or diverges.

Accepted Answer

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

Question 18

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

Question 19

Determine the values of x for which the function   can be replaced by the Taylor polynomial   if the error cannot exceed 0.006. Round your answer to four decimal places.

Accepted Answer

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

Question 20

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

Accepted Answer

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

Use a power series to approximate the value of the integral with an error less than 0.001. Round your answer to four decimal places.

Find the third Taylor polynomial for expanded about .

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

Find the radius of convergence of the power series.

Find the radius of convergence of the power series.

Write the repeating decimal as a geometric series.

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

Determine the convergence or divergence of the series .

Write the next two apparent terms of the sequence .

Find a power series for the function centered at 0.

Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places.

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

is the series diverges.

Determine the convergence or divergence of the series.

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

Use the Limit Comparison Test (if possible) 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.

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.006. Round your answer to four decimal places.

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

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 a power series to approximate the value of the integral with an error less than 0.001. Round your answer to four decimal places.

Find the third Taylor polynomial for expanded about .

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

Find the radius of convergence of the power series.

Find the radius of convergence of the power series.

Write the repeating decimal as a geometric series.

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

Determine the convergence or divergence of the series .

Write the next two apparent terms of the sequence .

Find a power series for the function centered at 0.

Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places. ​

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

is the series diverges.

Determine the convergence or divergence of the series.

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

Use the Limit Comparison Test (if possible) 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.

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.006. Round your answer to four decimal places.

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

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

Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places.