Verify the time-shifting property (3.16); that is,\[ x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \]\[ R' = R \]**Explanation:**- The equation \( x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \) represents the time-shifting property in the context of Laplace transforms. It states that if you shift a function in time by \( t_0 \), the Laplace transform is multiplied by an exponential factor \( e^{-st_0} \).- The expression \( R' = R \) implies that the region of convergence of the Laplace transform does not change with the time shift.

According to the definition of Laplace transform, following can be written:…

Answered: Verify the time-shifting property…

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Verify the time-shifting property (3.16); that is, sło X(s) R' = R (1 – 1)x

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Verify the time-shifting property (3.16); that is,

\[ x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \]

\[ R' = R \]

**Explanation:**

- The equation \( x(t - t_0) \longleftrightarrow e^{-st_0} X(s) \) represents the time-shifting property in the context of Laplace transforms. It states that if you shift a function in time by \( t_0 \), the Laplace transform is multiplied by an exponential factor \( e^{-st_0} \).

- The expression \( R' = R \) implies that the region of convergence of the Laplace transform does not change with the time shift.

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