Find the Laplace transform. Assume that a, b, and w are constants. 2. (a-bt) 6. e...

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● Find the Laplace transform. Assume that a, b, and w are constants. 2. (a-bt)² 6. e 'sinh4t (16.) 22. Existence. Show that L(1/√t) = √√/s. [Use (30) ) = √ in App. 3.1.] Conclude from this that the conditions in Theorem 3 are sufficient but not necessary for the existence of a Laplace transform. • Given F(s)=L(f), find f(t). a, b, L, n are constants. Show the details of your work. 1 28. (s + √2)(5-√3) • Find the laplace transform. 36. sinh t cos t . Find the inverse laplace transform. a(s + k) + bm (s + k)² + 77² 44 ● Find the Laplace transform. Assume that a, b, and w are constants. 2. (a-bt)² 6. e 'sinh4t (16.) 22. Existence. Show that L(1/√t) = √√/s. [Use (30) ) = √ in App. 3.1.] Conclude from this that the conditions in Theorem 3 are sufficient but not necessary for the existence of a Laplace transform. • Given F(s)=L(f), find f(t). a, b, L, n are constants. Show the details of your work. 1 28. (s + √2)(5-√3) • Find the laplace transform. 36. sinh t cos t . Find the inverse laplace transform. a(s + k) + bm (s + k)² + 77² 44

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