Program Explanation Given information: Transforms of derivatives theorem states that L { f ′ ( t ) } = s L { f ( t ) } − f ( 0 ) if the function f ( t ) is piecewise continuous. Similarly for second derivative of the function L { f ″ ( t ) } = s 2 L { f ( t ) } − s f ( 0 ) − f ′ ( 0 ) . The Laplace transform of t cos k t is written as, L { t cos k t } = s 2 − k 2 ( s 2 + k 2 ) 2 Calculation: Consider function f ( t ) as 1 2 k 3 ( sin k t − k t cos k t ) and obtain the Laplace transform as shown below. L { 1 2 k 3 ( sin k t − k t cos k t ) } = 1 2 k 3 L { sin k t − k t cos k t } L { 1 2 k 3 ( sin k t − k t cos k t ) } = 1 2 k 3 L { sin k t } − 1 2 k 2 L { t cos k t } L { 1 2 k 3 ( sin k t − k t cos k t ) } = 1 2 k 3 ( k s 2 + k 2 ) − 1 2 k 2 ( s 2 − k 2 ( s 2 + k 2 ) 2 ) L { 1 2 k 3 ( sin k t − k t cos k t ) } = 1 2 k 2 ( s 2 + k 2 ) − s 2 −

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ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 7.2, Problem 31P

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Program Description: Purpose of the problem is to show that L−1{1( s 2 + k 2 )2}=12k3(sinkt−ktcoskt) .

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Chapter 7.2, Problem 30P

Chapter 7.2, Problem 32P

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9. a) Determie values of a and b so that the function is continuous. ax - 2b f(x) 2 x≤-2 -2x+a, x ≥2 \-ax² - bx + 1, −2 < x < 2) 9b) Consider f(x): = 2x²+x-3 x-b and determine all the values of b such that f(x) does not have a vertical asymptote. Show work.

Chapter 7 Solutions

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Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of the problem is to show that L − 1 { 1 ( s 2 + k 2 ) 2 } = 1 2 k 3 ( sin k t − k t cos k t ) .

Solution Summary: The author explains the Laplace transform of tmathrmcoskt.

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Program Description: Purpose of the problem is to show that L−1{1( s 2 + k 2 )2}=12k3(sinkt−ktcoskt) .

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Chapter 7 Solutions