472 Appendix A Solutions to the Exercisrs ~ o ~ u t4.2 io~ Right-sitled functions have exponential mxkr, if 1L1, C and 7' can found such that: I.x(t)\ A l e r r for t T a) yes e.g with M = I, C = 1, T =0 5, T =0 b) yes, e.g w i t h ill = , C - c) yes e.g izritli M = I, C = 5, T - d) yes, e.g with AI = C = , 2' =- e ) no f ) yes, e.g witli M - I , r' = 0, T =0 ~ o l ~ ~ t4.3 ior~ First determine M , G, D a r i d T 50 that /.r(/)l5 Mc'" for I T anti l.r(t)l Me"' for t -T The bilaleral Laplace traiisform exists if the regioii ol' corierge1m is not rmpty, i.e if D > c' a) h f = I , C ' = a , D = O , T = O =+ R O C = { )