Question

Please do all parts please. thank you

Exercise 3. Let u(t) denote the unit step function u(t)= { 0, t<0, u(t)={ 1, ost. Show that A) (exp(at) u(t)) * (exp(Bt) u(t)) = ex (+)_exp(at) - exp(Bt) 8t) u(t), for a #B (1) a-B B) (exp(at)u(t)) * (exp(at)u(t))=texp(at)u(t) exp(Bt) - exp(at)+(a-B)texp(at)u(t), for a #B C) (t exp(at) u(t))*(exp(Bt) u(t))= (a - )2 D) (t exp(at)u(t)) * (exp(at)u(t)) =žt? exp(at)u(t) E) (t exp(at)u(t)) * (t exp(at)u(t)) = tº exp(at)u(t) (at)u(-t) +exp(Bt) u(t) for Rea) > Re(B) F) (exp(at) u(-)) * (exp(Bt) u(t)) = -B In part F) what happens if Re(a) <Re(B)? For the rest of the exercises you can manage with the above two tables.

Answer 1

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