Find the Laplace transform of the following

(a) finite support signals, and indicate their region of convergence:

(i) x(t) = δ(t − 1), 

(ii) y(t) = δ(t + 1) − δ(t − 1)

(iii) z(t) = u(t + 1) − u(t − 1), (iv) w(t) = cos(2π t) [u(t + 1) − u(t − 1)]

(b) causal signals, and indicate their region of convergence:­

(i) x₁(t) = e^−tu(t),               

(ii) y₁(t) = e^−tu(t − 1)

(iii) z₁(t) = e^−t+1u(t − 1),   

(iv) w₁(t) = e^−t(u(t) − u(t − 1))