LIte(0)I= S)F(S + α) = Lle-α f(t))1例l:L[te-α e(t)]格(S +a)S+α例2: Le cosate(t)] (S +α) + 五初值定理和终值定理LIcos ot] =+0f(t)在t=0处无冲激则初值定理：f(0t)= lim f(t) = lim SF(S)?800终值定理：lim f(t)存在时lim SF(S)=lim f(t)= f(o0)5-0
2 L[e cos t (t)] t 例 ： − 2 2 ( ) + + + = S S 2 ( ) 1 + = S 五.初值定理和终值定理 (0 ) lim ( ) lim ( ) 0 f f t SF S s t→ → + = = + 初值定理： f(t)在t = 0处无冲激则 F(S ) L[e f (t)] t − + = 1 L[te (t)] t 例 ： − lim f (t)存在时 t→ lim ( ) lim ( ) ( ) 0 = = → → SF S f t f s t 2 1 [ ( )] S L t t = 2 2 [cos ] + = s s L t 终值定理：
f (co) = lim f(t) = lim SF(S)S0证：利用导数性质f(t)e-" dt = lim[SF(S)-f(0-))lim0dtS-204f()lim e-"dt = f(gr-Y(0 )- lim SF(S)-f(0)S0S-03S2 +4S+5求f(0+)例1：已知F（S）S(S? + 2S+3)3S2 +4S+5=3= lims-0 (S + 2S +3)
( ) lim ( ) lim ( ) 0 f f t SF S t→ s→ = = 证：利用导数性质 lim ( ) lim[ ( ) (0 )] 0 0 0 − → − → − f t e dt = SF S − f dt d s st s f t e dt dt d st s − → − 0 0 ( )lim (0 ) ( 2 3) 3 4 5 1 ( ) 2 2 + + + + + = f S S S S S 例 ：已知F S 求 3 ( 2 3) 3 4 5 lim 2 2 = + + + + = → S S S S s = − 0 f ((t)) (0 ) lim ( ) (0 ) 0 − → − = f − f = SF S − f s