Question 1

The repeating decimal   is expressed as a geometric series   Write the decimal   as the ratio of two integers. ​​

Accepted Answer

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

Question 2

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 3

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

Accepted Answer

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

Question 4

​Apply Taylor's Theorem to find the power series centered at   for the function   ​

Accepted Answer

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

Question 5

​Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels. ​

Accepted Answer

A)  ​195 feet 
B)  ​82 feet 
C)  ​234 feet 
D)  ​111 feet 
E)  ​117 feet 
A)  ​195 feet 
B)  ​82 feet 
C)  ​234 feet 
D)  ​111 feet 
E)  ​117 feet

Question 6

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 7

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

Accepted Answer

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

Question 8

Find the third degree Taylor polynomial centered at   for the function. ​
​   ​

Accepted Answer

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

Question 9

​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 10

​Apply Taylor's Theorem to find the power series centered at   for the function   ​

Accepted Answer

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

Question 11

​You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer. ​

Accepted Answer

A)  ​$17,420,154 
B)  ​$1,000,000 
C)  ​$56,400 
D)  ​$360,000 
E)  ​$3,600 
A)  ​$17,420,154 
B)  ​$1,000,000 
C)  ​$56,400 
D)  ​$360,000 
E)  ​$3,600

Question 12

Determine the convergence or divergence of the following series. ​

Accepted Answer

A)  diverges 
B)  converges 
C)  inconclusive 
A)  diverges 
B)  converges 
C)  inconclusive

Question 13

A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river? ​

Accepted Answer

A)  180 ppm 
B)  ​90 ppm 
C)  ​85.35 ppm 
D)  705.88 ppm 
E)  ​100.41 ppm 
A)  180 ppm 
B)  ​90 ppm 
C)  ​85.35 ppm 
D)  705.88 ppm 
E)  ​100.41 ppm

Question 14

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 15

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 16

​Use a graphing utility to approximate all the real zeros of the function   by Newton's Method. ​

Accepted Answer

A)  ​-1.751, 2.028, 8.61 
B)  ​-1.151, 2.97, 9.707 
C)  ​-1.071, -1.391, -1.951 
D)  ​-1.231, 2.028, 9.736 
E)  ​-0.951,2.028,9.736 
A)  ​-1.751, 2.028, 8.61 
B)  ​-1.151, 2.97, 9.707 
C)  ​-1.071, -1.391, -1.951 
D)  ​-1.231, 2.028, 9.736 
E)  ​-0.951,2.028,9.736

Question 17

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 18

​Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8. ​   ​

Accepted Answer

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

Question 19

​Determine the convergence or divergence of the series   Use a symbolic algebra utility to verify your result. ​​

Accepted Answer

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

Question 20

A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years? ​

Accepted Answer

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

The repeating decimal is expressed as a geometric series Write the decimal as the ratio of two integers.

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

Determine the convergence or divergence of the following series.

Apply Taylor's Theorem to find the power series centered at for the function

Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels.

Find the limit of the following sequence.

Determine the convergence or divergence of the following series.

Find the third degree Taylor polynomial centered at for the function.

Determine the convergence or divergence of the p-series

Apply Taylor's Theorem to find the power series centered at for the function

You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer.

Determine the convergence or divergence of the following series.

A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river?

Find the limit of the following sequence.

Find the limit of the following sequence.

Use a graphing utility to approximate all the real zeros of the function by Newton's Method.

Find the limit of the following sequence.

Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years?

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

The repeating decimal is expressed as a geometric series Write the decimal as the ratio of two integers. ​​

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

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

​Apply Taylor's Theorem to find the power series centered at for the function ​

​Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels. ​

Find the limit of the following sequence. ​ ​

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

Find the third degree Taylor polynomial centered at for the function. ​ ​ ​

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

​Apply Taylor's Theorem to find the power series centered at for the function ​

​You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer. ​

Determine the convergence or divergence of the following series. ​

A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river? ​

Find the limit of the following sequence. ​ ​

Find the limit of the following sequence. ​ ​

​Use a graphing utility to approximate all the real zeros of the function by Newton's Method. ​

Find the limit of the following sequence. ​ ​

​Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8. ​ ​

​Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result. ​​

A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years? ​

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

The repeating decimal is expressed as a geometric series Write the decimal as the ratio of two integers.

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

Determine the convergence or divergence of the following series.

Apply Taylor's Theorem to find the power series centered at for the function

Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels.

Find the limit of the following sequence.

Determine the convergence or divergence of the following series.

Find the third degree Taylor polynomial centered at for the function.

Determine the convergence or divergence of the p-series

Apply Taylor's Theorem to find the power series centered at for the function

You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer.

Determine the convergence or divergence of the following series.

A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river?

Find the limit of the following sequence.

Find the limit of the following sequence.

Use a graphing utility to approximate all the real zeros of the function by Newton's Method.

Find the limit of the following sequence.

Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years?