586 Higher Engineering Mathematics
- (a) 2t−3(b)5t^2 + 4 t− 3
[
(a)
2
s^2
−
3
s
(b)
10
s^3
+
4
s^2
−
3
s
]
- (a)
t^3
24
− 3 t+2(b)
t^5
15
− 2 t^4 +
t^2
2
[
(a)
1
4 s^4
−
3
s^2
+
2
s
(b)
8
s^6
−
48
s^5
+
1
s^3
]
- (a) 5e^3 t(b) 2e−^2 t
[
(a)
5
s− 3
(b)
2
s+ 2
]
- (a) 4sin3t(b) 3cos2t
[
(a)
12
s^2 + 9
(b)
3 s
s^2 + 4
]
- (a) 7cosh2x(b)
1
3
sinh3t
[
(a)
7 s
s^2 − 4
(b)
1
s^2 − 9
]
- (a) 2cos^2 t(b) 3sin^22 x
[
(a)
2 (s^2 + 2 )
s(s^2 + 4 )
(b)
24
s(s^2 + 16 )
]
- (a) cosh^2 t(b) 2sinh^22 θ
[
(a)
s^2 − 2
s(s^2 − 4 )
(b)
16
s(s^2 − 16 )
]
- 4sin(at+b),whereaandbare constants.
[
4
s^2 +a^2
(acosb+ssinb)
]
- 3cos(ωt−α),whereωandαare constants.
[
3
s^2 +ω^2
(scosα+ωsinα)
]
- Show thatL(cos^23 t−sin^23 t)=
s
s^2 + 36