For positive numbers a < b, the pulse function is defined as (a) Sketch the graph of the pulse function. (b) Find the following limits:

For positive numbers a

(a) Sketch the graph of the pulse function.

(b) Find the following limits:

(i) lim _x→a+ P_a,b(x)

(ii) lim _x→a− P_a,b(x)

(iii) lim _x→b+ P_a,b(x)

(iv) lim _x→b− P_a,b(x)

(c) Discuss the continuity of the pulse function.

(d) Why is U(x)= 1/b − aP_a,b(x) called the unit pulse function?

[0. x < a Pab(x) = H(xa) - H(x - b) = 1, a x