Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both sides by e-kt, then transpose to show that for t 2 a. Then apply the mean value theorem to conclude that $(1) < ¢(a)ek(t-a) for t2 a.

Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both sides by e-kt, then transpose to show that for t 2 a. Then apply the mean value theorem to conclude that $(1) < ¢(a)ek(t-a) for t2 a.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both sides by e-kt, then transpose to show that for t 2 a. Then apply the mean value theorem to conclude that $(1) < ¢(a)ek(t-a) for t2 a.
Transcribed Image Text:Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both sides by e-kt, then transpose to show that for t 2 a. Then apply the mean value theorem to conclude that $(1) < ¢(a)ek(t-a) for t2 a.
Expert Solution
Step 1

Given: Suppose ϕ(t) is a differentiable function with ϕ'(t)≤kϕ(t) (k>0) such that ddtϕ(t)e-kt≤0.

To Prove: for t≥a , ϕ(t)≤ϕ(a)e(t-a)k.

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS