Explanation Given: The sequence a n = cos ( 0.99 n ) + 7 n + 9 n 63 n . Theorem used: The sequence { r n } converges to zero when − 1 < r < 1 . That is, lim n → ∞ r n = 0 if − 1 < r < 1 . Calculation: Compute, lim n → ∞ a n = lim n → ∞ cos ( 0.99 n ) + lim n → ∞ 7 n + 9 n 63 n (1) Obtain the limit of the sequence { cos ( 0.99 ) n } . Since 0.99 < 1 and by the result, lim n → ∞ ( 0.99 n ) = 0 . Here, the cosine function is continuous, lim n → ∞ ( cos ( 0.99 ) n ) = cos 0 Hence, lim n → ∞ ( cos ( 0.99 ) n ) = 1 (2) Compute the value of lim n → ∞ 7 n + 9 n 63 n

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

2nd Edition

ISBN: 9780321954237

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 8.2, Problem 81E

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To evaluate: The limit of the sequence or state that the limit does not exist.

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Chapter 8.2, Problem 80E

Chapter 8.2, Problem 82E

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Chapter 8 Solutions

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

Ch. 8.1 - Prob. 1QC Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - Prob. 5QC Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E

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The limit of the sequence or state that the limit does not exist.

Solution Summary: The author explains that the limit of the sequence is 0. Theorem used is leftrnright.

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To evaluate: The limit of the sequence or state that the limit does not exist.

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Chapter 8 Solutions