For the functions f(t) = et and g(t) = e 4t, defined on 0 < t < ∞, compute f g in two different ways: a. By directly evaluating the integral in the definition of f*g. (f* 9) (t) = f* b. By computing C-¹{F(s)G(s)} where F(s) = L{ƒ(t)} and G(s) = L{g(t)}. (f*g) (t) = L ¹{F(s)G(s)} = L ¹{ } = dw = help (formulas)
For the functions f(t) = et and g(t) = e 4t, defined on 0 < t < ∞, compute f g in two different ways: a. By directly evaluating the integral in the definition of f*g. (f* 9) (t) = f* b. By computing C-¹{F(s)G(s)} where F(s) = L{ƒ(t)} and G(s) = L{g(t)}. (f*g) (t) = L ¹{F(s)G(s)} = L ¹{ } = dw = help (formulas)
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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Transcribed Image Text:For the functions f(t) = et and g(t) = e 4t, defined on 0 < t < ∞, compute f g in two different ways:
a. By directly evaluating the integral in the definition of f*g.
(f* 9) (t) = f*
b. By computing C-¹{F(s)G(s)} where F(s) = L{ƒ(t)} and G(s) = L{g(t)}.
(f*g) (t) = L ¹{F(s)G(s)} = L ¹{
}
=
dw =
help (formulas)
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