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2. f(1) = 0/

2. f(1) = 0/

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
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**Problem 12:** Define the function \( f(t) \) as a piecewise function: - \( f(t) = e^{2t} \), for \( 0 < t < 3 \) - \( f(t) = 1 \), for \( 3 < t \) This function consists of two parts. For values of \( t \) between 0 and 3, \( f(t) \) follows the exponential function \( e^{2t} \). For values of \( t \) greater than 3, \( f(t) \) equals a constant value of 1. This kind of function is useful for representing different behaviors over different intervals of the variable \( t \).
Transcribed Image Text:**Problem 12:** Define the function \( f(t) \) as a piecewise function: - \( f(t) = e^{2t} \), for \( 0 < t < 3 \) - \( f(t) = 1 \), for \( 3 < t \) This function consists of two parts. For values of \( t \) between 0 and 3, \( f(t) \) follows the exponential function \( e^{2t} \). For values of \( t \) greater than 3, \( f(t) \) equals a constant value of 1. This kind of function is useful for representing different behaviors over different intervals of the variable \( t \).
In Problems 1–12, use Definition 1 to determine the Laplace transform of the given function.
Transcribed Image Text:In Problems 1–12, use Definition 1 to determine the Laplace transform of the given function.
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