Compute the Laplace Transforms of these functions explicitly (i.e., by directly computing 100⁰ € e-st f(t)dt): (a) f(t) = = ~ (b) f(t) = { -1, 0≤t<1 1, t> 1 t, 1, 0≤ t < 1 t≥1

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A: Formula of Laplace transform  Lu(t-c)=e-cssLtkf(t)=(-1)kdkdsk(F(s))

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A: Rewrite the given function as follows.…

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Q: FIS) = S-10 S2-65 + 8

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Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

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Q: The linear functional F: R^2[x] -&gt; R is defined by the formula F: p -&gt; ∫(from 1 to 0) p(t)dt.…

A: Step 1: Step 2: Step 3: Step 4:

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Q: Compute the Laplace transform of f(t) = ( 2, if 0 ≤ x &lt; 4 7t, if 4 ≤ x &lt; infinity)

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A: Let us solve both the problems one by one....

Q: Find the inverse Laplace transform f(t) = L{F(s)} of the function F(s) 5 2 s2 8 - 9 1) = c*{-(? 2 8…

A: We find inverse Laplace transform

Q: 11. Derive the inverse Laplace transform for 1 F(s) = (s + a)(s +b)' where b+ a.

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