SECTION 3.1 PROBLEMS 7. Q(s)= In each of Problems 1 through 5, use Table 3.1 to determine the Laplace transform of the function. 8. G(s)= - 9. P(s)= - 1. f(f)=3tcos(2t) 2. g(t) = e" sin(8t) 3. h(t) = 14t – sin(7t) 4. w(t) = cos(3t) – cos(7t) 5. k(t) = -5fe4+ sin(3t) In each of Problems 6 through 10, use Table 3.1 to (s+3)4 10. F(s)= 7 For Problems 11 through 14, suppose that f(t) is defined for all t>0 and has a period T. This means that f(t+ T)= f(t) for all t>0. 11. Show that determine the inverse Laplace transform of the function. EΓ" (a+1)T L[ f](s)= est 6. R(s)=.

SECTION 3.1 PROBLEMS In each of Problems 1 through 5, use Table 3.1 to determine the Laplace transform of the function. 1. f(1) =3t cos(21) 2. g(1) =e" sin(81) 3. h(t) =14t – sin(7t) 7. Q(s)= 8. G(s) = 9. P(s) = %3D 10. F(s) = For Problems 11 through 14, suppose that f(f) is defined for all t20 and has a period T. This means that f(t+T)= f(f) for all t> 0. 4. w(1) = cos(3f) –- cos(7t) 5. k(1) =-5fe+ sin(3f) In each of Problems 6 through 10, use Table 3.1 to determine the inverse Laplace transform of the function. 11. Show that 6. R(s) = LI F\(s) = E/ e f(t) dt.

3.3 using the fourier transform, f and g are in the first picture and the question is in the second