(a) Show that the function δ_ε(t) sketched in Figure 2.4(b) has unity area.

Figure 2.4 (b)

(b) Show that

δ_ε(t) = e^-1e^-t/εu(t)

has unity area. Sketch this function for E = 1,1/2, and 1/4. Comment on its suitability as an approximation for the unit impulse function.

(c) Show that a suitable approximation for the unit impulse function as ε †’ 0 is given by otherwise.

+0 1 -2 -1 (b) (1 |t| /e), |t|