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L {e-2 sin(2t) + e³¹12} L {(1+e-¹)2} L {tet cos(5t)}

L {e-2 sin(2t) + e³¹12} L {(1+e-¹)2} L {tet cos(5t)}

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image contains the following Laplace transforms: 1. **\[\mathcal{L}\{e^{-2t} \sin(2t) + e^{3t}t^2\}\]** This expression represents the Laplace transform of a function that consists of two components: an exponentially decaying sine function and a polynomial multiplied by an exponential function. 2. **\[\mathcal{L}\{(1 + e^{-t})^2\}\]** This expression is the Laplace transform of a function given by the square of the sum of 1 and an exponentially decaying term. 3. **\[\mathcal{L}\{te^{2t} \cos(5t)\}\]** This expression denotes the Laplace transform of a function that includes a linear term multiplied by an exponential function and a cosine function. These transforms are commonly used in engineering and mathematics to solve differential equations and analyze systems.
Transcribed Image Text:The image contains the following Laplace transforms: 1. **\[\mathcal{L}\{e^{-2t} \sin(2t) + e^{3t}t^2\}\]** This expression represents the Laplace transform of a function that consists of two components: an exponentially decaying sine function and a polynomial multiplied by an exponential function. 2. **\[\mathcal{L}\{(1 + e^{-t})^2\}\]** This expression is the Laplace transform of a function given by the square of the sum of 1 and an exponentially decaying term. 3. **\[\mathcal{L}\{te^{2t} \cos(5t)\}\]** This expression denotes the Laplace transform of a function that includes a linear term multiplied by an exponential function and a cosine function. These transforms are commonly used in engineering and mathematics to solve differential equations and analyze systems.
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