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Proof Let f be a positive, continues, and decreasing function for x ≥ 1 ,such that a n = f ( n ) . Prove that if the series ∑ n = 1 ∞ a n converges to S , then the reminder R N = S − S N is bounded by 0 ≤ R N ≤ ∫ N ∞ f ( x ) d x .

Proof Let f be a positive, continues, and decreasing function for x ≥ 1 ,such that a n = f ( n ) . Prove that if the series ∑ n = 1 ∞ a n converges to S , then the reminder R N = S − S N is bounded by 0 ≤ R N ≤ ∫ N ∞ f ( x ) d x .

Solution Summary: The author explains that the function f is a positive, decreasing and continuous function for xge 1.

Calculus

11th Edition

ISBN: 9780357246412

Author: Ron Larson; Bruce H. Edwards

Publisher: Cengage Limited

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Textbook Question

Chapter 9.3, Problem 51E

Proof Let f be a positive, continues, and decreasing function for x ≥ 1 ,such that a n = f ( n ) . Prove that if the series

∑ n = 1 ∞ a n

converges to S, then the reminder R N = S − S N is bounded by

0 ≤ R N ≤ ∫ N ∞ f ( x ) d x .

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Chapter 9.3, Problem 50E

Chapter 9.3, Problem 52E

Chapter 9 Solutions

Calculus

Ch. 9.1 - CONCEPT CHECK Recursively Defined Sequence What...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Writing the Terms of a Sequence In Exercises 510,...Ch. 9.1 - Prob. 6E Ch. 9.1 - Writing the Terms of a Sequence In Exercises 510,...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Writing the Terms of a Sequence In Exercises 11...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Matching In Exercises 13-16, match the sequence...Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Simplifying Factorials In Exercises 1720, simplify...Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Finding the Limit of a Sequence In Exercises 2124,...Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Prob. 43E Ch. 9.1 - Determining Convergence or Divergence In Exercises...Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Prob. 46E Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Prob. 48E Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Finding the n th Term of a Sequence In Exercises...Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Finding the nth Term of a Sequence In Exercises...Ch. 9.1 - Prob. 53E Ch. 9.1 - Prob. 54E Ch. 9.1 - Prob. 55E Ch. 9.1 - Monotonic and Bounded Sequences In Exercises...Ch. 9.1 - Prob. 57E Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - Prob. 61E Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Prob. 64E Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Government Expenditures A government program that...Ch. 9.1 - EXPLORING CONCEPTS Writing a Sequence Give an...Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - HOW DO YOU SEE IT? The graph, of two sequences are...Ch. 9.1 - Prob. 73E Ch. 9.1 - Prob. 74E Ch. 9.1 - Prob. 75E Ch. 9.1 - Prob. 76E Ch. 9.1 - Prob. 77E Ch. 9.1 - Prob. 78E Ch. 9.1 - Prob. 79E Ch. 9.1 - Prob. 80E Ch. 9.1 - Fibonacci Sequence In a study of the progeny of...Ch. 9.1 - Prob. 82E Ch. 9.1 - Prob. 83E Ch. 9.1 - Using a Sequence Consider the sequence an, where...Ch. 9.1 - Prob. 85E Ch. 9.1 - Prob. 86E Ch. 9.1 - Prob. 87E Ch. 9.1 - Prob. 88E Ch. 9.1 - Prob. 89E Ch. 9.1 - Prob. 90E Ch. 9.1 - Prob. 91E Ch. 9.2 - Sequence and Series Describe the difference...Ch. 9.2 - Geometric Series Define a geometric series, State...Ch. 9.2 - Limit of the nth term of a Series The limit of the...Ch. 9.2 - Prob. 4E Ch. 9.2 - Finding Partial Sums In Exercises 5-10, find the...Ch. 9.2 - Finding Partial Sums In Exercises 5-10, find the...Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Verifying Divergence In Exercises 11-18.verify...Ch. 9.2 - Verifying Divergence In Exercises 11-18.verify...Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Verifying Convergence In Excretes 19-24, verify...Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Prob. 31E Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Finding the Sum of a Convergent Series In...Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Using a Geometric Series In Exercises 3944, (a)...Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 48E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 50E Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Determining Convergence or Divergence In Exercises...Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - Prob. 60E Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - Prob. 63E Ch. 9.2 - Prob. 64E Ch. 9.2 - Making a Series Converge In Exercises 61-66, find...Ch. 9.2 - Prob. 66E Ch. 9.2 - Prob. 67E Ch. 9.2 - Prob. 68E Ch. 9.2 - Prob. 69E Ch. 9.2 - Prob. 70E Ch. 9.2 - Prob. 71E Ch. 9.2 - Prob. 72E Ch. 9.2 - Prob. 73E Ch. 9.2 - Prob. 74E Ch. 9.2 - Prob. 75E Ch. 9.2 - Prob. 76E Ch. 9.2 - Probability In Exercises 77 and 78, the random...Ch. 9.2 - Prob. 78E Ch. 9.2 - Probability A fair coin is tossed repeatedly. The...Ch. 9.2 - Prob. 80E Ch. 9.2 - Area The sides of a square are 16 inches in...Ch. 9.2 - Prob. 82E Ch. 9.2 - Prob. 83E Ch. 9.2 - Prob. 84E Ch. 9.2 - Prob. 85E Ch. 9.2 - Sphereflake The sphereflake shown below is a...Ch. 9.2 - Prob. 87E Ch. 9.2 - Prob. 88E Ch. 9.2 - Prob. 89E Ch. 9.2 - Prob. 90E Ch. 9.2 - Prob. 91E Ch. 9.2 - Prob. 92E Ch. 9.2 - Prob. 93E Ch. 9.2 - Prob. 94E Ch. 9.2 - Prob. 95E Ch. 9.2 - Prob. 96E Ch. 9.2 - Prob. 97E Ch. 9.2 - Proof Given two infinite series an and bn such...Ch. 9.2 - Prob. 99E Ch. 9.2 - Prob. 100E Ch. 9.2 - Prob. 101E Ch. 9.2 - Prob. 102E Ch. 9.2 - Prob. 103E Ch. 9.2 - Prob. 104E Ch. 9.3 - CONCEPT CHECK Integral Test What conditions have...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Prob. 16E Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 3-22, confirm...Ch. 9.3 - Using the Integral Test In Exercises 23 and 24,...Ch. 9.3 - Using the Integral Test In Exercises 23 and 24,...Ch. 9.3 - Conditions of the Integral Test In Exercises 2528,...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Conditions of the Integral Test In Exercises...Ch. 9.3 - Using the Integral Test In Exercises 29-32, use...Ch. 9.3 - Using the Integral Test In Exercises 29-32, use...Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Using a p -Series In Exercises 33-38, use Theorem...Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - Prob. 41E Ch. 9.3 - Prob. 42E Ch. 9.3 - Using a Series Use a graph to show that the...Ch. 9.3 - HOW DO YOU SEE IT? The graphs show the sequences...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 45-50 Find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Finding Values In Exercises 4550. find the...Ch. 9.3 - Finding Values In Exercises 45-50, find the...Ch. 9.3 - Proof Let f be a positive, continues, and...Ch. 9.3 - Using a Remainder Show that the results of...Ch. 9.3 - Approximating a Sum In Exercises 53-58, use the...Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Prob. 56E Ch. 9.3 - Prob. 57E Ch. 9.3 - Prob. 58E Ch. 9.3 - Finding a Value In Exercises 59-62, use the result...Ch. 9.3 - Prob. 60E Ch. 9.3 - Prob. 61E Ch. 9.3 - Finding a Value In Exercises 5962, use the result...Ch. 9.3 - Prob. 63E Ch. 9.3 - Prob. 64E Ch. 9.3 - Euler's Constant Let sn=k=1n1k=1+12+...+1n. (a)...Ch. 9.3 - Prob. 66E Ch. 9.3 - Prob. 67E Ch. 9.3 - Prob. 68E Ch. 9.3 - Prob. 69E Ch. 9.3 - Prob. 70E Ch. 9.3 - Prob. 71E Ch. 9.3 - Prob. 72E Ch. 9.3 - Prob. 73E Ch. 9.3 - Prob. 74E Ch. 9.3 - Prob. 75E Ch. 9.3 - Prob. 76E Ch. 9.3 - Prob. 77E Ch. 9.3 - Prob. 78E Ch. 9.3 - Prob. 79E Ch. 9.3 - Prob. 80E Ch. 9.4 - CONCEPT CHECK" Direct Comparison Test You want to...Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Using the Direct Comparison Test In Exercises...Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Using the Direct Comparison Test In Exercises...Ch. 9.4 - Prob. 17E Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Using the Limit Comparison Test In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Using the Limit Comparison Test Use die Limit...Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Determining Convergence or Divergence In Exercises...Ch. 9.4 - Prob. 45E Ch. 9.4 - Prob. 46E Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Prob. 50E Ch. 9.4 - Prob. 51E Ch. 9.4 - Prob. 52E Ch. 9.4 - Prob. 53E Ch. 9.4 - Prob. 54E Ch. 9.4 - Prob. 55E Ch. 9.4 - Prob. 56E Ch. 9.4 - Prob. 57E Ch. 9.4 - Prob. 58E Ch. 9.4 - Proof Prove that if the nonnegative series...Ch. 9.4 - Prob. 60E Ch. 9.4 - Finding Series Find two series that demonstrate...Ch. 9.4 - Prob. 62E Ch. 9.4 - Prob. 63E Ch. 9.4 - Prob. 64E Ch. 9.4 - Prob. 65E Ch. 9.4 - Verifying Divergence Use the result of Exercise 64...Ch. 9.4 - Prob. 67E Ch. 9.4 - Prob. 68E Ch. 9.4 - Prob. 69E Ch. 9.4 - Prob. 70E Ch. 9.4 - Prob. 71E Ch. 9.4 - Prob. 72E Ch. 9.5 - CONCEPT CHECK Alternating Series An alternating...Ch. 9.5 - Prob. 2E Ch. 9.5 - Absolute and Conditional Convergence In your own...Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Numerical and Graphical Analysis In Exercises 5-8,...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercise...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Determining Convergence or Divergence In Exercises...Ch. 9.5 - Approximating the Sum of an Alternating Series In...Ch. 9.5 - Approximating the Sum of an Alternating Series In...Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Finding the Number of Terms In Exercises 35-40,...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute and Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 48E Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 57E Ch. 9.5 - Determining Absolute end Conditional Convergence...Ch. 9.5 - Prob. 59E Ch. 9.5 - Prob. 60E Ch. 9.5 - Prob. 61E Ch. 9.5 - HOW DO YOU SEE IT? The graphs of the sequences of...Ch. 9.5 - Prob. 63E Ch. 9.5 - Prob. 64E Ch. 9.5 - Proof Prove that if | an | converges, then an2...Ch. 9.5 - Prob. 66E Ch. 9.5 - Prob. 67E Ch. 9.5 - Finding Values Find all values of x for which the...Ch. 9.5 - Prob. 69E Ch. 9.5 - Prob. 70E Ch. 9.5 - Prob. 71E Ch. 9.5 - Prob. 72E Ch. 9.5 - Prob. 73E Ch. 9.5 - Prob. 74E Ch. 9.5 - Prob. 75E Ch. 9.5 - Prob. 76E Ch. 9.5 - Prob. 77E Ch. 9.5 - Prob. 78E Ch. 9.5 - Prob. 79E Ch. 9.5 - Prob. 80E Ch. 9.5 - Prob. 81E Ch. 9.5 - Prob. 82E Ch. 9.6 - CONCEPT CHECK Ratio and Root Tests In Exercises...Ch. 9.6 - Prob. 2E Ch. 9.6 - Prob. 3E Ch. 9.6 - Prob. 4E Ch. 9.6 - Prob. 5E Ch. 9.6 - Prob. 6E Ch. 9.6 - Prob. 7E Ch. 9.6 - Prob. 8E Ch. 9.6 - Prob. 9E Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Matching In Exercises 9-14, match the series with...Ch. 9.6 - Prob. 14E Ch. 9.6 - Numerical, Graphical, and Analytic Analysis In...Ch. 9.6 - Prob. 16E Ch. 9.6 - Prob. 17E Ch. 9.6 - Prob. 18E Ch. 9.6 - Prob. 19E Ch. 9.6 - Prob. 20E Ch. 9.6 - Prob. 21E Ch. 9.6 - Prob. 22E Ch. 9.6 - Prob. 23E Ch. 9.6 - Prob. 24E Ch. 9.6 - Prob. 25E Ch. 9.6 - Prob. 26E Ch. 9.6 - Prob. 27E Ch. 9.6 - Using the Ratio Test In Exercises 17-38, use the...Ch. 9.6 - Prob. 29E Ch. 9.6 - Prob. 30E Ch. 9.6 - Prob. 31E Ch. 9.6 - Prob. 32E Ch. 9.6 - Prob. 33E Ch. 9.6 - Prob. 34E Ch. 9.6 - Prob. 35E Ch. 9.6 - Prob. 36E Ch. 9.6 - Using the Ratio Test In Exercises 17-38, use the...Ch. 9.6 - Prob. 38E Ch. 9.6 - Prob. 39E Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Prob. 41E Ch. 9.6 - Prob. 42E Ch. 9.6 - Prob. 43E Ch. 9.6 - Prob. 44E Ch. 9.6 - Prob. 45E Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Using the Root Test In Exercises 39-52, use the...Ch. 9.6 - Prob. 49E Ch. 9.6 - Prob. 50E Ch. 9.6 - Prob. 51E Ch. 9.6 - Prob. 52E Ch. 9.6 - Prob. 53E Ch. 9.6 - Prob. 54E Ch. 9.6 - Prob. 55E Ch. 9.6 - Prob. 56E Ch. 9.6 - Prob. 57E Ch. 9.6 - Prob. 58E Ch. 9.6 - Prob. 59E Ch. 9.6 - Review In Exercises 53-70, determine the...Ch. 9.6 - Prob. 61E Ch. 9.6 - Prob. 62E Ch. 9.6 - Prob. 63E Ch. 9.6 - Prob. 64E Ch. 9.6 - Prob. 65E Ch. 9.6 - Prob. 66E Ch. 9.6 - Prob. 67E Ch. 9.6 - Prob. 68E Ch. 9.6 - Prob. 69E Ch. 9.6 - Prob. 70E Ch. 9.6 - Prob. 71E Ch. 9.6 - Prob. 72E Ch. 9.6 - Prob. 73E Ch. 9.6 - Prob. 74E Ch. 9.6 - Prob. 75E Ch. 9.6 - Prob. 76E Ch. 9.6 - Prob. 77E Ch. 9.6 - Prob. 78E Ch. 9.6 - Prob. 79E Ch. 9.6 - Prob. 80E Ch. 9.6 - Prob. 81E Ch. 9.6 - Prob. 82E Ch. 9.6 - Prob. 83E Ch. 9.6 - Prob. 84E Ch. 9.6 - Prob. 85E Ch. 9.6 - Prob. 86E Ch. 9.6 - Prob. 87E Ch. 9.6 - Prob. 88E Ch. 9.6 - Prob. 89E Ch. 9.6 - Prob. 90E Ch. 9.6 - Prob. 91E Ch. 9.6 - Prob. 92E Ch. 9.6 - Prob. 93E Ch. 9.6 - Prob. 94E Ch. 9.6 - Prob. 95E Ch. 9.6 - Prob. 96E Ch. 9.6 - Prob. 97E Ch. 9.6 - Prob. 98E Ch. 9.6 - Prob. 99E Ch. 9.6 - Prob. 100E Ch. 9.6 - Prob. 101E Ch. 9.6 - Prob. 102E Ch. 9.6 - Prob. 103E Ch. 9.6 - Prob. 104E Ch. 9.6 - Prob. 105E Ch. 9.6 - Prob. 106E Ch. 9.6 - Prob. 107E Ch. 9.6 - Prob. 108E Ch. 9.7 - CONCEPT CHECK Polynomial Approximation An...Ch. 9.7 - Prob. 2E Ch. 9.7 - Prob. 3E Ch. 9.7 - Prob. 4E Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Prob. 7E Ch. 9.7 - Matching In Exercises 5-8, match the Taylor...Ch. 9.7 - Finding a First-Degree Polynomial Approximation In...Ch. 9.7 - Finding a First-Degree Polynomial Approximation In...Ch. 9.7 - Prob. 11E Ch. 9.7 - Prob. 12E Ch. 9.7 - Prob. 13E Ch. 9.7 - Prob. 14E Ch. 9.7 - Conjecture Consider the function f(x)=cosx and its...Ch. 9.7 - Conjecture Consider the function f(x)=x2ex. (a)...Ch. 9.7 - Prob. 17E Ch. 9.7 - Prob. 18E Ch. 9.7 - Prob. 19E Ch. 9.7 - Prob. 20E Ch. 9.7 - Prob. 21E Ch. 9.7 - Prob. 22E Ch. 9.7 - Prob. 23E Ch. 9.7 - Prob. 24E Ch. 9.7 - Prob. 25E Ch. 9.7 - Prob. 26E Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Finding a Taylor Polynomial In Exercises 27-32,...Ch. 9.7 - Prob. 30E Ch. 9.7 - Prob. 31E Ch. 9.7 - Prob. 32E Ch. 9.7 - Prob. 33E Ch. 9.7 - Prob. 34E Ch. 9.7 - Prob. 35E Ch. 9.7 - Prob. 36E Ch. 9.7 - Prob. 37E Ch. 9.7 - Prob. 38E Ch. 9.7 - Prob. 39E Ch. 9.7 - Prob. 40E Ch. 9.7 - Prob. 41E Ch. 9.7 - Prob. 42E Ch. 9.7 - Prob. 43E Ch. 9.7 - Prob. 44E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 46E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 48E Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Using Taylors Theorem In Exercises 45-50, use...Ch. 9.7 - Prob. 51E Ch. 9.7 - Prob. 52E Ch. 9.7 - Prob. 53E Ch. 9.7 - Prob. 54E Ch. 9.7 - Prob. 55E Ch. 9.7 - Prob. 56E Ch. 9.7 - Prob. 57E Ch. 9.7 - Prob. 58E Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Finding Values In Exercises 59-62, determine the...Ch. 9.7 - Prob. 62E Ch. 9.7 - Prob. 63E Ch. 9.7 - Prob. 64E Ch. 9.7 - Prob. 65E Ch. 9.7 - Prob. 66E Ch. 9.7 - Prob. 67E Ch. 9.7 - Differentiating Maclaurin Polynomials (a)...Ch. 9.7 - Prob. 69E Ch. 9.7 - Prob. 70E Ch. 9.7 - Prob. 71E Ch. 9.7 - Prob. 72E Ch. 9.7 - Prob. 73E Ch. 9.8 - Prob. 1E Ch. 9.8 - Prob. 2E Ch. 9.8 - Prob. 3E Ch. 9.8 - Prob. 4E Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Center of a Power Series In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercise...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercise...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Radius of Convergence In Exercises 39...Ch. 9.8 - Finding the Radius of Convergence In Exercises 39...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Prob. 43E Ch. 9.8 - Finding the Interval of Convergence In Exercises...Ch. 9.8 - Writing an Equivalent Series In Exercises 45-48,...Ch. 9.8 - Writing an Equivalent Series In Exercises 45-48,...Ch. 9.8 - Prob. 47E Ch. 9.8 - Prob. 48E Ch. 9.8 - Prob. 49E Ch. 9.8 - Finding Intervals of Convergence In Exercises...Ch. 9.8 - Prob. 51E Ch. 9.8 - Prob. 52E Ch. 9.8 - Prob. 53E Ch. 9.8 - Prob. 54E Ch. 9.8 - Prob. 55E Ch. 9.8 - Prob. 56E Ch. 9.8 - Using Power Series Let...Ch. 9.8 - Prob. 58E Ch. 9.8 - Prob. 59E Ch. 9.8 - Prob. 60E Ch. 9.8 - Prob. 61E Ch. 9.8 - Differential Equation In Exercises 59-64, show...Ch. 9.8 - Prob. 63E Ch. 9.8 - Prob. 64E Ch. 9.8 - Bessel Function The Bessel function of order 0 is...Ch. 9.8 - Prob. 66E Ch. 9.8 - Prob. 67E Ch. 9.8 - Investigation The interval of convergence of the...Ch. 9.8 - Prob. 69E Ch. 9.8 - Prob. 70E Ch. 9.8 - Identifying a Function In Exercises 69-72, the...Ch. 9.8 - Prob. 72E Ch. 9.8 - Prob. 73E Ch. 9.8 - Prob. 74E Ch. 9.8 - Prob. 75E Ch. 9.8 - Prob. 76E Ch. 9.8 - Proof Prove that the power series...Ch. 9.8 - Using a Power Series Let g(x)=1+2x+x2+2x3+x4+...Ch. 9.8 - Prob. 79E Ch. 9.8 - Proof Prove that if the power series n=0cnxn has a...Ch. 9.8 - Prob. 81E Ch. 9.9 - Prob. 1E Ch. 9.9 - Prob. 2E Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Geometric Power Series In Exercises 3-6,...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 13E Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 17E Ch. 9.9 - Finding a Power Series In Exercises 7-18, find a...Ch. 9.9 - Prob. 19E Ch. 9.9 - Prob. 20E Ch. 9.9 - Prob. 21E Ch. 9.9 - Prob. 22E Ch. 9.9 - Using a Power Series In Exercises 19-28, use the...Ch. 9.9 - Using a Power Series In Exercises 19-28, use the...Ch. 9.9 - Prob. 25E Ch. 9.9 - Prob. 26E Ch. 9.9 - Prob. 27E Ch. 9.9 - Prob. 28E Ch. 9.9 - Prob. 29E Ch. 9.9 - Prob. 30E Ch. 9.9 - Prob. 31E Ch. 9.9 - Prob. 32E Ch. 9.9 - Prob. 33E Ch. 9.9 - Prob. 34E Ch. 9.9 - Prob. 35E Ch. 9.9 - Prob. 36E Ch. 9.9 - Prob. 37E Ch. 9.9 - Using a Power Series In Exercises 37-40, use the...Ch. 9.9 - Prob. 39E Ch. 9.9 - Prob. 40E Ch. 9.9 - Prob. 41E Ch. 9.9 - Prob. 42E Ch. 9.9 - Prob. 43E Ch. 9.9 - Prob. 44E Ch. 9.9 - Prob. 45E Ch. 9.9 - Prob. 46E Ch. 9.9 - Prob. 47E Ch. 9.9 - Prob. 48E Ch. 9.9 - Prob. 49E Ch. 9.9 - Prob. 50E Ch. 9.9 - Prob. 51E Ch. 9.9 - Prob. 52E Ch. 9.9 - Prob. 53E Ch. 9.9 - Prob. 54E Ch. 9.9 - Prob. 55E Ch. 9.9 - Prob. 56E Ch. 9.9 - Prob. 57E Ch. 9.10 - Prob. 1E Ch. 9.10 - Prob. 2E Ch. 9.10 - Prob. 3E Ch. 9.10 - Finding a Taylor Series Explain how to use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 13E Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 15E Ch. 9.10 - Finding a Taylor Series In Exercises 5-16, use the...Ch. 9.10 - Prob. 17E Ch. 9.10 - Prob. 18E Ch. 9.10 - Prob. 19E Ch. 9.10 - Prob. 20E Ch. 9.10 - Prob. 21E Ch. 9.10 - Prob. 22E Ch. 9.10 - Using a Binomial Series In Exercises 21-26, use...Ch. 9.10 - Prob. 24E Ch. 9.10 - Prob. 25E Ch. 9.10 - Prob. 26E Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Prob. 28E Ch. 9.10 - Prob. 29E Ch. 9.10 - Prob. 30E Ch. 9.10 - Prob. 31E Ch. 9.10 - Prob. 32E Ch. 9.10 - Prob. 33E Ch. 9.10 - Prob. 34E Ch. 9.10 - Prob. 35E Ch. 9.10 - Prob. 36E Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Finding a Maclaurin Series In Exercises 27-40,...Ch. 9.10 - Prob. 39E Ch. 9.10 - Prob. 40E Ch. 9.10 - Prob. 41E Ch. 9.10 - Prob. 42E Ch. 9.10 - Prob. 43E Ch. 9.10 - Prob. 44E Ch. 9.10 - Prob. 45E Ch. 9.10 - Prob. 46E Ch. 9.10 - Prob. 47E Ch. 9.10 - Prob. 48E Ch. 9.10 - Prob. 49E Ch. 9.10 - Prob. 50E Ch. 9.10 - Prob. 51E Ch. 9.10 - Prob. 52E Ch. 9.10 - Prob. 53E Ch. 9.10 - Prob. 54E Ch. 9.10 - Prob. 55E Ch. 9.10 - Prob. 56E Ch. 9.10 - Prob. 57E Ch. 9.10 - Prob. 58E Ch. 9.10 - Finding a Limit In Exercises 59-62, use the series...Ch. 9.10 - Prob. 60E Ch. 9.10 - Prob. 61E Ch. 9.10 - Prob. 62E Ch. 9.10 - Prob. 63E Ch. 9.10 - Prob. 64E Ch. 9.10 - Approximating an Integral In Exercises 63-70, use...Ch. 9.10 - Prob. 66E Ch. 9.10 - Prob. 67E Ch. 9.10 - Prob. 68E Ch. 9.10 - Prob. 69E Ch. 9.10 - Prob. 70E Ch. 9.10 - Prob. 71E Ch. 9.10 - Prob. 72E Ch. 9.10 - Prob. 73E Ch. 9.10 - Prob. 74E Ch. 9.10 - Prob. 75E Ch. 9.10 - Prob. 76E Ch. 9.10 - Prob. 77E Ch. 9.10 - Prob. 78E Ch. 9.10 - Projectile Motion A projectile fired from the...Ch. 9.10 - Prob. 80E Ch. 9.10 - Prob. 81E Ch. 9.10 - Prob. 82E Ch. 9.10 - Prob. 83E Ch. 9.10 - Prob. 84E Ch. 9.10 - Prob. 85E Ch. 9.10 - Prob. 86E Ch. 9.10 - Prob. 87E Ch. 9.10 - Prob. 88E Ch. 9.10 - Prob. 89E Ch. 9.10 - Prob. 90E Ch. 9.10 - Prob. 91E Ch. 9.10 - Using Fibonacci Numbers Show that the Maclaurin...Ch. 9.10 - Prob. 93E Ch. 9 - Writing the Terms of a Sequence In Exercises 1-4,...Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Determining Convergence or Divergence In Exercises...Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Finding Partial Sums In Exercises 27 and 28, find...Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71RE Ch. 9 - Prob. 72RE Ch. 9 - Prob. 73RE Ch. 9 - Prob. 74RE Ch. 9 - Prob. 75RE Ch. 9 - Prob. 76RE Ch. 9 - Prob. 77RE Ch. 9 - Prob. 78RE Ch. 9 - Prob. 79RE Ch. 9 - Prob. 80RE Ch. 9 - Prob. 81RE Ch. 9 - Prob. 82RE Ch. 9 - Prob. 83RE Ch. 9 - Prob. 84RE Ch. 9 - Prob. 85RE Ch. 9 - Prob. 86RE Ch. 9 - Prob. 87RE Ch. 9 - Prob. 88RE Ch. 9 - Prob. 89RE Ch. 9 - Finding Intervals of Convergence In Exercises 89...Ch. 9 - Prob. 91RE Ch. 9 - Prob. 92RE Ch. 9 - Finding a Geometric Power Series In Exercises 93...Ch. 9 - Prob. 94RE Ch. 9 - Prob. 95RE Ch. 9 - Prob. 96RE Ch. 9 - Prob. 97RE Ch. 9 - Prob. 98RE Ch. 9 - Prob. 99RE Ch. 9 - Prob. 100RE Ch. 9 - Prob. 101RE Ch. 9 - Prob. 102RE Ch. 9 - Finding a Taylor Series In Exercises 103-110, use...Ch. 9 - Finding a Taylor Series In Exercises 103-110, use...Ch. 9 - Prob. 105RE Ch. 9 - Prob. 106RE Ch. 9 - Prob. 107RE Ch. 9 - Prob. 108RE Ch. 9 - Finding a Taylor SeriesIn Exercises 103-110, use...Ch. 9 - Prob. 110RE Ch. 9 - Prob. 111RE Ch. 9 - Prob. 112RE Ch. 9 - Prob. 113RE Ch. 9 - Prob. 114RE Ch. 9 - Prob. 115RE Ch. 9 - Prob. 116RE Ch. 9 - Prob. 117RE Ch. 9 - Prob. 118RE Ch. 9 - Prob. 1PS Ch. 9 - Prob. 2PS Ch. 9 - Prob. 3PS Ch. 9 - Finding a Limit Let T be an equilateral triangle...Ch. 9 - Prob. 5PS Ch. 9 - Prob. 6PS Ch. 9 - Prob. 7PS Ch. 9 - Prob. 8PS Ch. 9 - Prob. 9PS Ch. 9 - Prob. 10PS Ch. 9 - Prob. 11PS Ch. 9 - Prob. 12PS Ch. 9 - Prob. 13PS Ch. 9 - Prob. 14PS Ch. 9 - Prob. 15PS Ch. 9 - Prob. 16PS

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