3 Given that the Laplace transform of x is F(3) 1
derive the
Laplace transform of xl without using the integral definition
4 Use the Laplace transform to volve each of the following equations.
(a) f(x) + f(x) = x where f(0) = 0
(b) f(x) -x) = where f(0) = -1
(c) '(x) + 48*(x) + 4) where 0 = 0 and (0) - 0
(d) 48" (x) - 9f(x) = -18 where f(0) = 0 and f(0) 0
3 Show that if F() - )
xxx then:
(a) () F() L()) m (*) - 110
Use part (a) to find
(b) 01 Lsin 2x) ir 11x cos3x)
(c) What would you say the mh derivative of Fs) is equal to?
4 Show that it (x)} F($) then La) F's - A) where is a
constant
Hunce hind
(a) (sinha)
(b) cosbx) where a and b are constants in both cases