Let f(t) be a function on [0,00). The Laplace transform of f is the function F defined by the integral F(s) = e - S'f(t) dt. Use this definition to determine the Laplace transform of the following function. f(t) = e 5t The Laplace transform of f(t) is F(s) =

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

Let f(t) be a function on (0, oo). The Laplace transform of f is the function E defined by the integral F(s) = e St(t)dt. Use this definition to determine the Laplace transform of the foliowing function. f(1) = e -41 sin 3t The Laplace transform of f(t) is F(s)= (Type an expression using s as the variable.) It is defined for s> (Type an integer or a fraction.)