, L T . .
f(t) < 2[f(H5 =
F(s)
2 [f (+ )] = f(s) =
]"f(t) Estat
Examples .
01 .
f(t) = 1
f(s) =
) " xStdt =
[st]" = -
+ (0 ) 1
- =
; So
02 .
f (t) = t
F(s)
= testy
=fjest)
=
-(0 - 0) + - esta
=
0
+x
=
se
, 03 ·
f(t) = th
method O : Use the induction method
method 8 : Using Gamma function .
r(x) =
! "t Et de r(n 1)
+
= n !
f(s) =
) "th Estat
Let's assume z =
st (S)0) Et =
Els
dz = Sdt t to zfo
=> dt =
tdz t z-0
-
F(s)
=(dz = jozdz 8
- -dz x(utis
=
She
04 · f(t) = eat
F(s) =
]are stated tea
= (0 - 1)
S-a
a
, eso = cosc +
jSinO
To =
coo-jSinO
05 . f(t) =
Sin(at)
since)
= seat-in
F(s)
=arjat
= "Sinlatest de
Cetts-ja) existin]dt
=
-
aa
· [sjae es-ja)ot letis I
-
g
= (sija-stja) = Stia-Stim
S2 + al
= a
S2 + 92
0 f(t) = Cos (at)
cos(at)
= Seating
F(s)
= "Sinlatest de
=earjat)
= [Cetts-ja) + exist
ja)]dt
-[sja es-ja)o letistaat I
-
e
=
(sja +
stja) =
+ Stjarsja
S2 + al
= S
S2 + 92
f(t) < 2[f(H5 =
F(s)
2 [f (+ )] = f(s) =
]"f(t) Estat
Examples .
01 .
f(t) = 1
f(s) =
) " xStdt =
[st]" = -
+ (0 ) 1
- =
; So
02 .
f (t) = t
F(s)
= testy
=fjest)
=
-(0 - 0) + - esta
=
0
+x
=
se
, 03 ·
f(t) = th
method O : Use the induction method
method 8 : Using Gamma function .
r(x) =
! "t Et de r(n 1)
+
= n !
f(s) =
) "th Estat
Let's assume z =
st (S)0) Et =
Els
dz = Sdt t to zfo
=> dt =
tdz t z-0
-
F(s)
=(dz = jozdz 8
- -dz x(utis
=
She
04 · f(t) = eat
F(s) =
]are stated tea
= (0 - 1)
S-a
a
, eso = cosc +
jSinO
To =
coo-jSinO
05 . f(t) =
Sin(at)
since)
= seat-in
F(s)
=arjat
= "Sinlatest de
Cetts-ja) existin]dt
=
-
aa
· [sjae es-ja)ot letis I
-
g
= (sija-stja) = Stia-Stim
S2 + al
= a
S2 + 92
0 f(t) = Cos (at)
cos(at)
= Seating
F(s)
= "Sinlatest de
=earjat)
= [Cetts-ja) + exist
ja)]dt
-[sja es-ja)o letistaat I
-
e
=
(sja +
stja) =
+ Stjarsja
S2 + al
= S
S2 + 92
