1. Find a formula for the general term of the sequence, assuming that the pattern of the first few
terms continues.
2. Find the partial sum of the series . Give your answer to five decimal places.
3. How many terms of
...
1. Find a formula for the general term of the sequence, assuming that the pattern of the first few
terms continues.
2. Find the partial sum of the series . Give your answer to five decimal places.
3. How many terms of the series would you need to add to find its sum to within
0.02?
4. Test the series for convergence or divergence.
5. Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.
6. Test the series for convergence or divergence.
7. Test the series for convergence or divergence.
8. Use the binomial series to expand the function as a power series. Find the radius of convergence.Stewart - Calculus ET 8e Chapter 11 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
9. Find the sum of the series.
10. Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of
values of x for which the given approximation is accurate to within the stated error.
Write a such that .
11. Write the first five terms of the sequence whose term is given.
12. Find an expression for the term of the sequence. (Assume that the pattern continues.)
13. Determine whether the given series converges or diverges. If it converges, find its sum.
14. Determine whether the given series is convergent or divergent.
15. Determine whether the series converges or diverges.Stewart - Calculus ET 8e Chapter 11 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
16. Test the series for convergence or divergence.
17. Determine whether the series converges or diverges.
18. Determine whether the series is convergent or divergent.
19. Determine whether the series is convergent or divergent.
20. Determine whether the series is convergent or divergent.Stewart - Calculus ET 8e Chapter 11 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3.
4. convergent
5.
6. divergent
7. divergent
8.
9.
10.
11.
12.
13.
14. Convergent
15. Converges
16. Convergent
17. Converges
18. converges
19. convergent
20. convergentStewart - Calculus ET 8e Chapter 11 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Determine whether the sequence converges or diverges. If it converges, find the limit.
2. Find the exact value of the limit of the sequence defined by .
3. The terms of a series are defined recursively by the equations .
Determine whether converges or diverges.
4. Express the number as a ratio of integers.
5. Use the Integral Test to determine whether the series is convergent or divergent.
6. How many terms of the series would you need to add to find its sum to within
0.02?
7. Test the series for convergence or divergence.
8. Determine whether the sequence convergent or divergent.
9. Test the series for convergence or divergence.Stewart - Calculus ET 8e Chapter 11 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
10. Test the series for convergence or divergence.
11. Find a power series representation for the function and determine the radius of convergence.
12. Find the Maclaurin series for using the definition of a Maclaurin serires.
13. Use the binomial series to expand the function as a power series. Find the radius of convergence.
14. Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of
values of x for which the given approximation is accurate to within the stated error.
Write a such that .
15. Use the sum of the first 9 terms to approximate the sum of the following series.
Write your answer to six decimal places.
16. Determine whether the series is convergent or divergent.Stewart - Calculus ET 8e Chapter 11 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
17. Determine whether the series converges or diverges.
18. Determine whether the series is convergent or divergent.
19. Determine whether the series is convergent or divergent.
20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.Stewart - Calculus ET 8e Chapter 11 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3. diverges
4. 9
11
5. divergent
6.
7. convergent
8. converges
9. convergent
10. convergent
11.
12.
13.
14.
15.
16. Convergent
17. Diverges
18. Convergent
19. converges
20. conditionally convergentStewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
a.
b. –5
c.
d. Diverges
____ 2. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
a. 1
b.
c. 0
d. Diverges
____ 3. Find the value of the limit for the sequence given.
a.
b.
c.
d.
e.Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 4. If $600 is invested at interest, compounded annually, then after n years the investment is
worth dollars. Find the size of investment after 7 years.
a. $430.21
b. $1,860.81
c. $1,230.81
d. $789.56
e. $1,321.06
____ 5. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 30
b. 36
c. 5
d. Diverges
____ 6. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence.
a.
b. 14
c.
d.
e. 15Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a.
b.
c. Diverges
d.
____ 8. Find all positive values of u for which the series converges.
a.
b.
c.
d.
e.Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 9. Determine which one of the p-series below is divergent.
a.
b.
c.
d.
____ 10. Find an approximation of the sum of the series accurate to two decimal places.
a. –1.06
b. –0.84
c. –0.90
d. –0.98
____ 11. Approximate the sum to the indicated accuracy.
(five decimal places)
a.
b.
c.
d.
e.Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 12. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 13. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 14. Find the interval of convergence of the series.
a.
b.
c.
d. diverges everywhere
e.Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 15. Find a power series representation for
a.
b.
c.
d.
e.
____ 16. Use the power series for to estimate correct to four decimal places.
a.
b.
c.
d.
e.
____ 17. Use series to approximate the definite integral to within the indicated accuracy.
a. 0.0354
b. 0.0125
c. 0.0625
d. 0.1447
e. 0.2774Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. Use series to evaluate the limit correct to three decimal places.
Select the correct answer.
a. 118.933
b. 114.133
c. 34.3233
d. 114.333
e. 115.933
____ 19. For which positive integers k is the series convergent?
a.
b.
c.
d.
e.
____ 20. Which of the given series are absolutely convergent?
a.
b.Stewart – Calculus ET 8e Chapter 11 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2. C
3. A
4. D
5. B
6. B
7. D
8. C
9. A
10. C
11. D
12. D
13. B
14. C
15. B
16. A
17. A
18. D
19. A
20. BStewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Find the value of the limit for the sequence given.
a.
b.
c.
d.
e.
____ 2. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
a. 13
b. 5
c. Diverges
d. –3
____ 3. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 12
b. Diverges
c. 3
d. 16
____ 4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
a. 30
b. 36
c. 5
d. DivergesStewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 5. A rubber ball is dropped from a height of 8 m onto a flat surface. Each time the ball hits the
surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.
a. 16
b. 24
c. 8
d. 32
____ 6. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence.
a.
b. 14
c.
d.
e. 15
____ 7. Find the sum of the series.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 8. Find all positive values of u for which the series converges.
a.
b.
c.
d.
e.
____ 9. Find all values of p for which the series converges.
a.
b.
c.
d.
____ 10. Determine whether the sequence convergent or divergent.
a. converges
b. diverges
____ 11. Test the series for convergence or divergence.
a. The series is convergent.
b. The series is divergent.Stewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 12. Determine which series is convergent.
a.
b.
____ 13. Find the values of p for which the series is convergent.
a.
b.
c.
d.
____ 14. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 15. Suppose that the radius of convergence of the power series is . What is the radius of
convergence of the power series .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 16. Find the radius of convergence and the interval of convergence of the power series.
a.
b.
c.
d.
____ 17. Find the Maclaurin series for f (x) using the definition of the Maclaurin series.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin
series for the function.
a.
b.
c.
d.
e.
____ 19. Given the series estimate the error in using the partial sum by comparison
with the series .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
a. conditionally convergent
b. absolutely convergent
c. divergentStewart - Calculus ET 8e Chapter 11 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2. C
3. D
4. B
5. B
6. B
7. C
8. C
9. D
10. A
11. A
12. B
13. B
14. D
15. B
16. A
17. D
18. B
19. C
20. BStewart - Calculus ET 8e Chapter 11 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
____ 2. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit. Select the correct answer.
a. 13
b. 5
c. Diverges
d. –3
3. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit.
4. Determine whether the series is convergent or divergent by expressing as a telescoping sum. If
it is convergent, find its sum.
.
5. Determine whether the geometric series converges or diverges. If it converges, find its sum.
____ 6. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence. Select the correct answer.
a.
b. 14
c.
d.
e. 15
7. Determine which one of the p-series below is convergent.
8. Determine which one of the p-series below is divergent.Stewart - Calculus ET 8e Chapter 11 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
9. Let where f is a continuous, positive, and decreasing function on and suppose
that is convergent. Defining where and we have that
Find the maximum error if the sum of the series is
approximated by
____ 10. Test the series for convergence or divergence. Select the correct answer.
a. The series is convergent.
b. The series is divergent.
11. Approximate the sum to the indicated accuracy.
(five decimal places)
12. Find the radius of convergence and the interval of convergence of the power series.
13. Find the radius of convergence and the interval of convergence of the power series.Stewart - Calculus ET 8e Chapter 11 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 14. Find the radius of convergence and the interval of convergence of the power series.
Select the correct answer.
a.
b.
c.
d.
15. Use the power series for to estimate correct to four decimal places.
16. Use series to evaluate the limit correct to three decimal places.
Select the correct answer.
17. Use the binomial series to expand the function as a power series. Find the radius of convergence.
18. Given the series estimate the error in using the partial sum by comparison
with the series .
____ 19. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Select the correct answer.
a. conditionally convergent
b. absolutely convergent
c. divergentStewart - Calculus ET 8e Chapter 11 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.Stewart - Calculus ET 8e Chapter 11 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2. C
3. 0
4.
5. 36
6. B
7.
8.
9. 0.075
10. A
11.
12.
13.
14. B
15.
16. 114.333
17.
18.
19. C
20. absolutely convergent© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 11 Form F
____ 1. Determine whether the sequence defined by converges or diverges. If it converges,
find its limit. Select the correct answer.
a.
b. –5
c.
d. Diverges
2. Determine whether the sequence converges or diverges. If it converges, find the limit.
____ 3. Find the value of the limit for the sequence given. Select the correct answer.
a.
b.
c.
d.
e.
4. If $600 is invested at interest, compounded annually, then after n years the investment is
worth dollars. Find the size of investment after 7 years.
5. A sequenceis defined recursively by the equation for where
.
Use your calculator to guess the limit of the sequence.
6. Determine whether the geometric series converges or diverges. If it converges, find its sum.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. When money is spent on goods and services, those that receive the money also spend some of it.
The people receiving some of the twice-spent money will spend some of that, and so on.
Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the
local government begins the process by spending D dollars. Suppose that each recipient of spent
money spends and saves of the money that he or she receives. The values c and s
are called the marginal propensity to consume and the marginal propensity to save and, of course,
.
The number k = 1/s is called the multiplier. What is the multiplier if the marginal propensity to
consume is ?
Select the correct answer.
a. 4
b. 3
c. 6
d. 7
e. 10
8. Find the sum of the series.
9. Find an approximation of the sum of the series accurate to two decimal places.
____ 10. Determine which series is convergent. Select the correct answer.
a.
b.
11. Approximate the sum to the indicated accuracy.
(five decimal places)© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12. Find the radius of convergence and the interval of convergence of the power series.
____ 13. Find the radius of convergence and the interval of convergence of the power series. \
Select the correct answer.
a.
b.
c.
d.
14. Suppose that the radius of convergence of the power series is . What is the radius of
convergence of the power series .
15. Find the radius of convergence and the interval of convergence of the power series.
____ 16. Find the radius of convergence of the series. Select the correct answer.
a.
b.
c.
d.
e.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
17. Use series to evaluate the limit correct to three decimal places.
Select the correct answer.
18. Given the series estimate the error in using the partial sum by comparison
with the series .
____ 19. For which positive integers k is the series convergent? Select the correct answer.
a.
b.
c.
d.
e.
____ 20. Which of the given series are absolutely convergent? Select the correct answer.
a.
b.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2.
3. A
4. $789.56
5. 14
6.
7. E
8.
9. –0.90
10. B
11.
12.
13. B
14.
15.
16. D
17. 114.333
18.
19. A
20. BStewart - Calculus ET 8e Chapter 11 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Find the value of the limit of the sequence defined by
.
Select the correct answer.
a.
b.
c.
d.
e.
2. Determine whether the sequence converges or diverges. If it converges, find the limit.
3. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
____ 4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
Select the correct answer.
a. 12
b. Diverges
c. 3
d. 16Stewart - Calculus ET 8e Chapter 11 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
5. Determine whether the given series converges or diverges. If it converges, find its sum.
6. Determine whether the given series converges or diverges. If it converges, find its sum.
7. Determine which one of the p-series below is convergent.
____ 8. How many terms of the series do we need to add in order to find the sum to the indicated
accuracy? Select the correct answer.
a.
b.
c.
d.
e.
9. Find an approximation of the sum of the series accurate to two decimal places.
10. Determine which series is convergent.
____ 11. Find the values of p for which the series is convergent. Select the correct answer.
a.
b.
c.
d.Stewart - Calculus ET 8e Chapter 11 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12. Find the radius of convergence and the interval of convergence of the power series.
13. Find the interval of convergence of the series.
14. Find the radius of convergence of the series.
____ 15. Find the radius of convergence of the series. Select the correct answer.
a.
b.
c.
d.
e.
16. Find a power series representation for the function.
17. Find a power series representation for
18. Find the Maclaurin series for f (x) using the definition of the Maclaurin series.Stewart - Calculus ET 8e Chapter 11 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19. For which positive integers k is the series convergent?
____ 20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Select the correct answer.
a. conditionally convergent
b. absolutely convergent
c. divergentStewart - Calculus ET 8e Chapter 11 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2.
3. Diverges
4. D
5. Diverges
6. Diverges
7.
8. A
9. –0.90
10.
11. B
12.
13.
14.
15. D
16.
17.
18.
19.
20. BStewart – Calculus ET 8e Chapter 11 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Find the value of the limit for the sequence given. Select the correct answer.
a.
b.
c.
d.
e.
2. If $600 is invested at interest, compounded annually, then after n years the investment is
worth dollars. Find the size of investment after 7 years.
3. Determine whether the given series converges or diverges. If it converges, find its sum.
4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
____ 5. A rubber ball is dropped from a height of 8 m onto a flat surface. Each time the ball hits the
surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.
Select the correct answer.
a. 16
b. 24
c. 8
d. 32
6. Determine whether the geometric series converges or diverges. If it converges, find its sum.
7. Determine whether the given series converges or diverges. If it converges, find its sum.Stewart – Calculus ET 8e Chapter 11 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 8. Find all positive values of u for which the series converges. Select the correct answer.
a.
b.
c.
d.
e.
9. Find all values of p for which the series converges.
10. Test the series for convergence or divergence.
11. Find an approximation of the sum of the series accurate to two decimal places.
12. Approximate the sum to the indicated accuracy.
(five decimal places)Stewart – Calculus ET 8e Chapter 11 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 13. Find the radius of convergence and the interval of convergence of the power series. ]
Select the correct answer.
a.
b.
c.
d.
14. Find the radius of convergence and the interval of convergence of the power series.
____ 15. Find the interval of convergence of the series. Select the correct answer.
a.
b.
c.
d. diverges everywhere
e.
16. Find the radius of convergence of the series.
17. Find a power series representation for the function.Stewart – Calculus ET 8e Chapter 11 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 18. Use the power series for to estimate correct to four decimal places.
Select the correct answer.
a.
b.
c.
d.
e.
19. Given the series estimate the error in using the partial sum by comparison
with the series .
____ 20. Evaluate the function by a Taylor polynomial of degree centered at , and
.
Select the correct answer.
a.
b.
c.
d.
e.Stewart – Calculus ET 8e Chapter 11 Form H
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2. $789.56
3. Diverges
4. 36
5. B
6.
7. Diverges
8. C
9.
10. The series is convergent.
11. –0.90
12.
13. B
14.
15. C
16.
17.
18. A
19.
20. A
[Show More]
.png)
.png)
.png)
.png)
.png)
