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
3sinh3t
[
(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