Program Description: Purpose of the problem is to show that ϕ ( t ) ≤ ϕ ( a ) e k ( t − a ) for t ≥ a , if ϕ ( t ) is differentiable with ϕ ′ ( t ) ≤ k ϕ ( t ) for t ≥ a such that k > 0 .

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Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Answer 2

Question

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Answer 3

Question

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Answer 4

Question

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Answer 5

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

Answer 6

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

Answer 7

Chapter A.5, Problem 18P

Program Plan Intro

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

Answer 8

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Answer 9

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Answer 11

Ch. A.5 - In Problems 1 through 8, compute the successive...Ch. A.5 - Prob. 2P Ch. A.5 - Prob. 3P Ch. A.5 - Prob. 4P Ch. A.5 - Prob. 5P Ch. A.5 - Prob. 6P Ch. A.5 - Prob. 7P Ch. A.5 - Prob. 8P Ch. A.5 - Prob. 9P Ch. A.5 - Prob. 10P

Program Description: Purpose of the problem is to show that ϕ ( t ) ≤ ϕ ( a ) e k ( t − a ) for t ≥ a , if ϕ ( t ) is differentiable with ϕ ′ ( t ) ≤ k ϕ ( t ) for t ≥ a such that k > 0 .

Solution Summary: The author explains the function varphi(t) is a differentiable, if it's the same as e-kt.

Concept explainers

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Chapter A Solutions

Program Description: Purpose of the problem is to show that ϕ ( t ) ≤ ϕ ( a ) e k ( t − a ) for t ≥ a , if ϕ ( t ) is differentiable with ϕ ′ ( t ) ≤ k ϕ ( t ) for t ≥ a such that k &gt; 0 .

Solution Summary: The author explains the function varphi(t) is a differentiable, if it's the same as e-kt.

Concept explainers

Program Description: Purpose of the problem is to show that ϕ(t)≤ϕ(a)ek(t−a) for t≥a , if ϕ(t) is differentiable with ϕ′(t)≤kϕ(t) for t≥a such that k>0 .

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Chapter A Solutions

Program Description: Purpose of the problem is to show that ϕ ( t ) ≤ ϕ ( a ) e k ( t − a ) for t ≥ a , if ϕ ( t ) is differentiable with ϕ ′ ( t ) ≤ k ϕ ( t ) for t ≥ a such that k > 0 .