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1. Come up with a combination of Heaviside functions whose graph: has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter.

1. Come up with a combination of Heaviside functions whose graph: has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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Please explain how to do 1. a, b and c. Final answers are given.
Final Answers: a) 3u(t-4) - u(t - 6) b) 8-9u(t-1) + u(t - 2) c) t+ (1 - t)u(t - 4) d) sin(t) + sin(t)u(t - 2π) e) 2u(t-1) + (-2t+4)u(t-2) + (2t - 6)u(t - 3) f) Σu(t-n), t > 0 ∞ n=1 ∞ g) 1+u(t-n), t ≥ 0 n=1 h) Σ 2u(t - n),t 20 n=1 220
Transcribed Image Text:Final Answers: a) 3u(t-4) - u(t - 6) b) 8-9u(t-1) + u(t - 2) c) t+ (1 - t)u(t - 4) d) sin(t) + sin(t)u(t - 2π) e) 2u(t-1) + (-2t+4)u(t-2) + (2t - 6)u(t - 3) f) Σu(t-n), t > 0 ∞ n=1 ∞ g) 1+u(t-n), t ≥ 0 n=1 h) Σ 2u(t - n),t 20 n=1 220
1. Come up with a combination of Heaviside functions whose graph: a) has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter. d) follows the curve y = sin(t) until t = 27, and then follows y = e) looks like this: 2 O 1 2 3 2 sin(t) thereafter. t
Transcribed Image Text:1. Come up with a combination of Heaviside functions whose graph: a) has a constant height of 0 until t = 4, jumps up to 3 until t = 6, and then falls to 2 thereafter. b) has a constant height of 8 until t = 1, falls to -1 from t = 1 to t = 2, and has a height of 0 thereafter. c) follows the line y = t until t = 4, and then has a height of 1 thereafter. d) follows the curve y = sin(t) until t = 27, and then follows y = e) looks like this: 2 O 1 2 3 2 sin(t) thereafter. t
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