Determine an inverse Laplace transform of the function. a) **[0-3,²]- 3e 4³²- b)

1 Practice with Fourier Transforms (**) For the listed functions A) through D), do the following: • Plot the function f(x) and its magnitude |ƒ(x)|. • Compute the Fourier transform of f(x): A) f(x) = e-|x| 1, B) f(x) = { 1 g(k) |x| ≤ 1 | • Compute and plot the magnitude |g(k)| as a function of k. • For each function and its transform, think about (but do not compute!) Parseval's Theorem: lg(k)|²dk = |f(x)|²da 0, otherwise = -∞ 1 √2π Lx f(x)e-iker dar (1) Based on your drawings of the function and its Fourier transform, which side of Parseval's theorem would be easier to compute? (2)

B GL definition of latlace transform use The to find [{+²H (E-5)}

-1, 0st<1 Draw a graph of f(t) and then use the definition to find the Laplace 121 transform of f(t).