Answered: Prove the following: i. f(t) * g(t) =…

Prove the following: i. f(t) * g(t) = g(t) * f(t). ii. If f and g are piecewise continuous and of exponential order on [0, 0), then (f * g)(t) is of exponential order on [0, ∞0).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Problem 4: Prove the Following:**

i. $ f(t) \ast g(t) = g(t) \ast f(t) $.

ii. If $ f $ and $ g $ are piecewise continuous and of exponential order on $[0, \infty)$, then $(f \ast g)(t)$ is of exponential order on $[0, \infty)$.

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