Question 1

Write the first five terms of the sequence. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 2

​Approximate the sum of the convergent series   using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places. ​
​

Accepted Answer

A)  ​The approximate value is 1.0286.
The maximum error of your approximation is 0.0084. 
B)  ​​The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.​ 
C)  ​​The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.​ 
D)  ​​The approximate value is 2.0023.
The maximum error of your approximation is ​1.0023. 
E)  ​​​The approximate value is 1.0812.
The maximum error of your approximation is ​0.0069. 
A)  ​The approximate value is 1.0286.
The maximum error of your approximation is 0.0084. 
B)  ​​The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.​ 
C)  ​​The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.​ 
D)  ​​The approximate value is 2.0023.
The maximum error of your approximation is ​1.0023. 
E)  ​​​The approximate value is 1.0812.
The maximum error of your approximation is ​0.0069.

Question 3

​Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places. ​     ​

Accepted Answer

A)  ​0.371 
B)  ​0.363 
C)  ​0.356 
D)  ​0.359 
E)  ​0.352 
A)  ​0.371 
B)  ​0.363 
C)  ​0.356 
D)  ​0.359 
E)  ​0.352

Question 4

Find the limit of the following sequence. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The limit does not exist. 
A)    
B)    
C)    
D)    
E)  The limit does not exist.

Question 5

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

Accepted Answer

A)  ​5 ,   ,   ,   ,   
B)  ​​5 ,   ,   ,   ,   
C)  ​​5 ,   ,   ,   ,   
D)  ​​5 ,   ,   , 321 ,   
E)  ​​5 ,   ,   ,   ,   
A)  ​5 ,   ,   ,   ,   
B)  ​​5 ,   ,   ,   ,   
C)  ​​5 ,   ,   ,   ,   
D)  ​​5 ,   ,   , 321 ,   
E)  ​​5 ,   ,   ,   ,

Question 6

Find the limit of the sequence   ​

Accepted Answer

A)    
B)  1 
C)  0 
D)    
E)  The limit does not exist. 
A)    
B)  1 
C)  0 
D)    
E)  The limit does not exist.

Question 7

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​     ​

Accepted Answer

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

Question 8

Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.]   ​ ​​

Accepted Answer

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

Question 9

Determine the convergence or divergence of the sequence   If the sequence converges,use a symbolic algebra utility to find its limit. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The sequence diverges. 
A)    
B)    
C)    
D)    
E)  The sequence diverges.

Question 10

​Determine the convergence or divergence of the following series. ​   ​

Accepted Answer

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

Question 11

Determine the convergence or divergence of the p-series

Accepted Answer

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

Question 12

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​     ​
​   ​

Accepted Answer

A)  ​2.898 
B)  ​2.893 
C)  ​2.888 
D)  ​2.843 
E)  ​2.943 
A)  ​2.898 
B)  ​2.893 
C)  ​2.888 
D)  ​2.843 
E)  ​2.943

Question 13

​Find the power series for the function   using the power series for   ​

Accepted Answer

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

Question 14

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​     ​
​   ​

Accepted Answer

A)  ​0.574 
B)  ​0.564 
C)  ​0.569 
D)  ​0.519 
E)  ​0.619 
A)  ​0.574 
B)  ​0.564 
C)  ​0.569 
D)  ​0.519 
E)  ​0.619

Question 15

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

Accepted Answer

A)  ​Diverges. 
B)  Converges. 
C)  ​Ratio Test is inconclusive. 
A)  ​Diverges. 
B)  Converges. 
C)  ​Ratio Test is inconclusive.

Question 16

​Determine the convergence or divergence of the p-series   ​

Accepted Answer

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

Question 17

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​   ​   ​

Accepted Answer

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

Question 18

​The ordering and transportation cost C of the components used in manufacturing a product is given by   where C is measured in thousands of dollars and x is the order size in hundreds.Find the order size that minimizes the cost.Round your answer to the nearest unit. ​

Accepted Answer

A)  ​58 hundreds 
B)  ​56 hundreds 
C)  ​53 hundreds 
D)  ​55 hundreds 
E)  ​60 hundreds 
A)  ​58 hundreds 
B)  ​56 hundreds 
C)  ​53 hundreds 
D)  ​55 hundreds 
E)  ​60 hundreds

Question 19

​Consider the sequence   whose nth term is given by   where P is the principal,   is the amount of compound interest after n months,and ​r is the annual percentage rate.Write the first four terms of the sequence for   and   Round your answer to two decimal places. ​

Accepted Answer

A)  ​9,563.33, 9,637.22, 9,716.38, 9,755.88 
B)  ​​9,564.34, 9,637.22, 9,716.38, 9,789.25 
C)  ​​9,563.33, 9,627.09, 9,691.27, 9,755.88 
D)  ​​9,564.34, 9,637.22, 9,691.27, 9,755.88 
E)  ​​9,564.34,9,627.09,9,691.27,9,789.25 
A)  ​9,563.33, 9,637.22, 9,716.38, 9,755.88 
B)  ​​9,564.34, 9,637.22, 9,716.38, 9,789.25 
C)  ​​9,563.33, 9,627.09, 9,691.27, 9,755.88 
D)  ​​9,564.34, 9,637.22, 9,691.27, 9,755.88 
E)  ​​9,564.34,9,627.09,9,691.27,9,789.25

Question 20

​Use Newton´s Method to approximate the zero(s)of the function   accurate to three decimal places. ​

Accepted Answer

A)  ​1.12 
B)  ​1.124 
C)  ​-1.12 
D)  ​-1.124 
E)  ​1.113 
A)  ​1.12 
B)  ​1.124 
C)  ​-1.12 
D)  ​-1.124 
E)  ​1.113

Write the first five terms of the sequence.

Approximate the sum of the convergent series using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.

Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places.

Find the limit of the following sequence.

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

Find the limit of the sequence

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] $Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] $

Determine the convergence or divergence of the sequence If the sequence converges,use a symbolic algebra utility to find its limit.

Determine the convergence or divergence of the following series.

Determine the convergence or divergence of the p-series

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Find the power series for the function using the power series for

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

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

Determine the convergence or divergence of the p-series

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

The ordering and transportation cost C of the components used in manufacturing a product is given by where C is measured in thousands of dollars and x is the order size in hundreds.Find the order size that minimizes the cost.Round your answer to the nearest unit.

Consider the sequence whose nth term is given by where P is the principal, is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places.

Use Newton´s Method to approximate the zero(s)of the function accurate to three decimal places.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Exam 10: Series and Taylor Polynomials

Write the first five terms of the sequence. ​ ​

​Approximate the sum of the convergent series using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places. ​ ​

​Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places. ​ ​

Find the limit of the following sequence. ​ ​

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

Find the limit of the sequence ​

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​

Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] ​ ​​

Determine the convergence or divergence of the sequence If the sequence converges,use a symbolic algebra utility to find its limit. ​

​Determine the convergence or divergence of the following series. ​ ​

Determine the convergence or divergence of the p-series

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​ ​ ​ ​

​Find the power series for the function using the power series for ​

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​ ​ ​ ​

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

​Determine the convergence or divergence of the p-series ​

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails. ​ ​ ​

​The ordering and transportation cost C of the components used in manufacturing a product is given by where C is measured in thousands of dollars and x is the order size in hundreds.Find the order size that minimizes the cost.Round your answer to the nearest unit. ​

​Consider the sequence whose nth term is given by where P is the principal, is the amount of compound interest after n months,and ​r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places. ​

​Use Newton´s Method to approximate the zero(s)of the function accurate to three decimal places. ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Write the first five terms of the sequence.

Approximate the sum of the convergent series using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.

Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places.

Find the limit of the following sequence.

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

Find the limit of the sequence

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] $Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] $

Determine the convergence or divergence of the sequence If the sequence converges,use a symbolic algebra utility to find its limit.

Determine the convergence or divergence of the following series.

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Find the power series for the function using the power series for

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

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

Determine the convergence or divergence of the p-series

The value for which Newton's method fails for the function below is shown in the graph.Give the reason why the method fails.

The ordering and transportation cost C of the components used in manufacturing a product is given by where C is measured in thousands of dollars and x is the order size in hundreds.Find the order size that minimizes the cost.Round your answer to the nearest unit.

Consider the sequence whose nth term is given by where P is the principal, is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places.

Use Newton´s Method to approximate the zero(s)of the function accurate to three decimal places.