586 Higher Engineering Mathematics
1. (a) 2t − 3 (b) 5t 2 + 4t − 3
(a)
2
s 2 −
3
s
(b)
10
s 3 +
4
s 2 −
3
s
2. (a)
t 3
24
− 3t + 2 (b)
t 5
15
− 2t
4
+
t 2
2
(a)
1
4s 4 −
3
s 2 +
2
s
(b)
8
s 6 −
48
s 5 +
1
s 3
3. (a) 5e
3t (b) 2e −2t
(a)
5
s − 3
(b)
2
s + 2
4. (a) 4 sin 3t (b) 3 cos2t
(a)
12
s 2 + 9
(b)
3s
s 2 + 4
5. (a) 7 cosh 2x (b)
1
3
sinh 3t
(a)
7s
s 2 − 4
(b)
1
s 2 − 9
6. (a) 2 cos
2 t (b) 3 sin
2 2x
(a)
2(s
2
+ 2)
s(s 2 + 4)
(b)
24
s(s 2 + 16)
7. (a) cosh
2 t (b) 2 sinh 2 2θ
(a)
s 2 − 2
s(s 2 − 4)
(b)
16
s(s 2 − 16)
8. 4 sin(at + b), where a and b are constants.
4
s 2 + a 2 (a cos b + s sin b)
9. 3 cos(ωt − α), where ω and α are constants.
3
s 2 + ω 2 (s cos α + ω sin α)
10. Show that L(cos
2 3t − sin
2 3t ) =
s
s 2 + 36