Chapter 9 Approximate The Sum The Series Using The

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subject Textbook Calculus: Early Transcendental Functions 6th Edition
subject Authors Bruce H. Edwards, Ron Larson
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9.3 The Integral Test and p-Series
554
b. k e.
c.
____ 14. Find the positive values of for which the series converges.
converges for
diverges only at
converges for
converges for
converges for
____ 15. Find the positive values of for which the series converges.
The series converges for .
The series converges for .
The series diverges for all positive values of .
The series converges for .
The series converges for .
555 Chapter 9: Infinite Series
____ 16. Determine the convergence or divergence of the series.
converges
diverges
cannot be determined
____ 17. Determine the convergence or divergence of the series.
converges
diverges
cannot be determined
____ 18. Determine the convergence or divergence of the series.
converges
diverges
cannot be determined
page-pf3
9.3 The Integral Test and p-Series
556
9.3 The Integral Test and p-Series
Answer Section
557 Chapter 9: Infinite Series
9.4 Comparisons of Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the Direct Comparison Test (if possible) to determine whether the series
converges or diverges.
converges
diverges
____ 2. Use the Direct Comparison Test to determine the convergence or divergence of the
series .
a.
b.
____ 3. Use the Direct Comparison Test (if possible) to determine whether the series
converges
diverges
____ 4. Use the Direct Comparison Test (if possible) to determine whether the series
converges or diverges.
diverges
converges
9.4 Comparisons of Series
558
____ 5. Use the Direct Comparison Test to determine the convergence or divergence of the
series .
a.
b.
____ 6. Use the Direct Comparison Test to determine the convergence or divergence of the
series
a.
b.
____ 7. Use the Direct Comparison Test to determine the convergence or divergence of the
series .
a.
b.
____ 8. Use the Limit Comparison Test to determine the convergence or divergence of the
series .
a.
b.
559 Chapter 9: Infinite Series
____ 9. Use the Limit Comparison Test (if possible) to determine whether the series
.
diverges
converges
c.
____ 10. Use the Limit Comparison Test to determine the convergence or divergence of the
series .
a.
b.
____ 11. Use the Limit Comparison Test (if possible) to determine whether the series
converges or diverges.
diverges
converges
____ 12. Use the Limit Comparison Test (if possible) to determine whether the series
converges or diverges.
converges
diverges
____ 13. Use the Limit Comparison Test to determine the convergence or divergence of the
series .
a.
b.
9.4 Comparisons of Series
560
____
14.
Use the Limit Comparison Test to determine the convergence or divergence of the
series
.
a.
b.
____
15.
Use the Limit Comparison Test to determine the convergence or divergence of the
series
.
a.
b.
____
16.
Use the Direct Comparison Test to determine the convergence or divergence
of the series
.
a.
b.
____ 17. Use the polynomial test to determine whether the series
converges or diverges.
a.
b.
561 Chapter 9: Infinite Series
____ 18. Use the polynomial test to determine whether the series converges or
diverges.
a.
b.
____ 19. Determine the convergence or divergence of the series
.
a.
b.
____ 20. Determine the convergence or divergence of the series .
a.
b.
____ 21.
Consider the series
. The sum of the series is
Find the sum of
the series
.
a.
1.5932
b.
1.5632
c.
1.6132
d.
1.6232
e.
1.5732
page-pf9
9.4 Comparisons of Series
562
9.4 Comparisons of Series
Answer Section
563 Chapter 9: Infinite Series
9.5 Alternating Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. True or false: The series converges.
a.
b.
____ 2. True or false: The series diverges.
a.
b.
____ 3. True or false: The series converges.
a.
b.
____ 4. True or false: The series converges .
a.
b.
____ 5. Determine whether the series converges conditionally or
absolutely, or diverges.
The series converges conditionally but does not converge absolutely.
The series converges absolutely but does not converge conditionally.
The series diverges.
The series converges absolutely.
9.5 Alternating Series
564
____ 6. Determine whether the series converges absolutely, converges
conditionally, or diverges.
diverges
____ 7. Determine whether the series converges conditionally or
absolutely, or diverges.
The series converges absolutely.
The series diverges.
The series converges absolutely but does not converge conditionally.
The series converges conditionally but does not converge absolutely.
____ 8. Determine whether the series converges conditionally or
absolutely, or diverges.
The series converges absolutely.
The series diverges.
The series converges absolutely but does not converge conditionally.
The series converges conditionally but does not converge absolutely.
____ 9. Approximate the sum of the series by using the first six terms.
1.457 < S < 1.477
1.417 < S < 1.497
1.467 < S < 1.472
1.427 < S < 1.467
1.461 < S < 1.473
____ 10. Approximate the sum of the series by using the first six terms.
1.799 < S < 1.805
1.794 < S < 1.806
1.794 < S < 1.805
1.792 < S < 1.792
565
Chapter 9: Infinite Series
e. 1.698 < S < 1.902
____
11.
Determine the minimal number of terms required to approximate the sum of the
series with an error of less than 0.007.
5
4
2
6
3
____ 12. Determine the minimal number of terms required to approximate the sum of the series
with an error of less than 0.004.
10
5
8
6
4
____ 13. Determine the minimal number of terms required to approximate the sum of the series
with an error of less than 0.008.
3
1
4
6
2
____ 14. Determine the minimal number of terms required to approximate the sum of the series
with an error of less than 0.005.
6
4
5
8
3
9.5 Alternating Series
566
____ 15. Approximate the sum of the series by using the first six terms.
0.587 < S < 3.473
1.549 < S < 2.511
1.309 < S < 2.751
0.427 < S < 3.633
0.227 < S < 3.833
page-pfe
567 Chapter 9: Infinite Series
9.5 Alternating Series
Answer Section
9.6 The Ratio and Root Test
568
9.6 The Ratio and Root Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the Ratio Test to determine the convergence or divergence of the series .
a.
b.
____ 2. Use the Ratio Test to determine the convergence or divergence of the series.
diverges
Ratio Test inconclusive
converges
____ 3. Use the Ratio Test to determine the convergence or divergence of the series.
converges
diverges
____ 4. Use the Ratio Test to determine the convergence or divergence of the series.
diverges
converges
Ratio Test inconclusive
569 Chapter 9: Infinite Series
____ 5. Use the Ratio Test to determine the convergence or divergence of the series
.
a.
b.
____ 6. Use the Root Test to determine the convergence or divergence of the series .
a.
b.
____ 7. Use the Root Test to determine the convergence or divergence of the series.
converges
diverges
Root Test inconclusive
____ 8. Use the Root Test to determine the convergence or divergence of the series.
converges
diverges
Root Test inconclusive
____ 9. Use the Root Test to determine the convergence or divergence of the series.
Root Test inconclusive
converges
diverges
9.6 The Ratio and Root Test
570
____ 10. Use the Root Test to determine the convergence or divergence of the series .
converges
diverges
____ 11. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
____ 12. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 13. Determine the convergence or divergence of the series using any appropriate test from
this chapter. Identify the test used.
a.
b.
c.
d.
e.
____ 14. Determine the convergence or divergence of the series using any appropriate test from
this chapter. Identify the test used.
converges; Ratio Test
both civerges; p-series and civerges; Integral Test
civerges; p-series
civerges; Integral Test
converges; p-series
571
Chapter 9: Infinite Series
____
15.
Determine the convergence or divergence of the series using any appropriate test
from this chapter. Identify the test used.
both diverges; Ratio Test and diverges; Theorem 9.9 (nth Term Test for Divergence)
converges; Integral Test
diverges; Theorem 9.9 (nth Term Test for Divergence)
converges; p-series
diverges; Ratio Test
____ 16. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
____ 17. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 18. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
9.6 The Ratio and Root Test
572
____ 19.
Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 20. The terms of a series are defined recursively. Determine the convergence or
divergence of the series. Explain your reasoning.
converges; Ratio Test
diverges; Ratio Test
diverges; Integral Test
converges; Alternating Series Test
converges; Root Test
____ 21. Find the values of x for which the series converges.
a.
b.
c.
d.
e.
____ 22. Find the values of x for which the series converges.
a.
b.
c.
d.
e.
page-pf14
573 Chapter 9: Infinite Series
9.6 The Ratio and Root Test
Answer Section

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