For positive numbers a < b, the pulse function is defined as 0, x < a 1, a sx < b 0, x 2 b Pab(x) = H(x – a) – H(x – b) = x 2 0 is the Heaviside function. lo, ´1, where H(x) x < 0 (a) Sketch the graph of the pulse function. (b) Find the following limits: (i) lim Pub(x) (ii) lim Pa,(x) ха * a* (iii) lim P(x) * b+ (iv) lim Pa(x) b- (c) Discuss the continuity of the pulse function. 1 (d) Why is U(x) = Pab(x) called the unit pulse function? b - a

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