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Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/8 1- e-sT

Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/8 1- e-sT

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/s 1- e-sT
Transcribed Image Text:Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/s 1- e-sT
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