(a) Give reasons why Theorems 1 and 2 are more important than Theorem 3. (b) Extend Theorem...
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(b) Extend Theorem 1 by showing that if f(t) is continuous, except for an ordinary discontinuity (finite jump) at some t = α (>0) the other conditions remaining as in Theorem 1, then (see Fig. 117)
(1*) L(f') = sL(f) - f(0) - [f(α + 0) - f(α - 0)]e-αs
(c) Verify (1*) for f(t) = e-t if 0 < t < 1 and 0 if and 0 if t > 1.
Transcribed Image Text:
f(e) -f(a-0) f(a + 0) Formula (1*) Fig. 117.
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