Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral LARE)} = | e-strt) dt is said to be the Laplace transform of f, provided that the integral converge Find {f{t)}. (Write your answer as a function of s.) {Rt)} = (s > 0) f(t) + (2, 2) 1

Q: Let Rt) be the inverse Laplace transform of 7s2 + 15s – 6 F(s) = (s? + 6s + 10)(s – 2) What is 3/2)?

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Q: -2x jika x > 0 jika x <0 f(x) =

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Q: 2. Calculate the inverse Laplace transform: 2s (a) C- C-¹ { 25+32 }; (b) C-¹ ( 25-3₂} 2s L-1

A: We have to find the Laplace inverse transformation of and

Q: Find Fourier transform for : A) f(t) = e-3t cos² (3t) B) f(t) = te tu(t - 3)

A: (A)Given f(t)=e−3tcos2⁡(3t).Now, we'll find the Fourier transforms for individual terms.The Fourier…

Q: F(s) = 1 (s + 1)²(s² + 4)

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Q: Let ft) be the inverse Laplace transform of 7s2 + 9s + 30 F(s) = (s2 + 4s + 5)(s – 5)" What is…

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Q: {e-3t+ et cos 4t}

A: Evaluate Laplace transform:  Le-3t+etcos4t

Q: (3.5) of the 3.1 Definition and Basic Properties 2. Use the definition of the Laplace transform to…

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Q: Show that the Fourier sine transform of the function 0 < x≤1 {:- 1-x 1 ≤ x ≤ 2 2≤x is given by 2 sin…

A: I think the given answer is not correct.

Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms L{f(t)} and n = 1, 2, 3, . . . , then If…

A: Please find the answer in next step