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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Transcribed Image Text: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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