(c) Translate the pulse, i.e. move the nonzero value of the func- tion to a different location while maintaining the width [for example, let f(t) = 1 for 1 ≤ t ≤ 2 and zero elsewhere; then try for f(t) = 1 for 2 ≤ t ≤ 3 and zero elsewhere; and so on.] Show that it obeys the translation property of Laplace Transforms, L{f(ta)} = e-as F (s). (d) Widen the pulse, i.e. keep the other eage at zero and in- crease the width of the nonzero value [for example, extend to f(t) = 1 for 0 ≤ t ≤ 2 and zero elsewhere; the do for f(t) = 1 for 0 ≤ t ≤ 3 and zero elsewhere]. Show that you can get the scaling property of the Laplace Transform, L {f(at)} = F (₁).

Use the second translation theorem to find the Laplace transform of g(t)=θ(t−1)(t2+3t+2) .

Compute the Laplace Transform of f(t) = e-5t using the definition of the transform. (Just listing the transform from the table will not get you any points).