In each of Problem 9 through 24, use the linearity of L-1, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function: 1.2.f(t) = L-¹{F(s)}1t", n = positive integer3.4. t,p>-15.sin at6.cos at7. sinh at8. cosh at9. et sin bt10. et cos bt11. teat, n positive integer=12. uc(t)13. uc(t)f(t-c)14. et f(t)15. Sof(t-1) g(7) dr16. (t-c)17. f(n) (t)18. t" f(t)F(s) = £{f(t)}7,8>0."s > agm+1; 8>0r(p+1)8>0ਕ, 8 > 0+) 8>0>8> |a|8> |a|(8-4)³² +6²8-4(s-a)² +6²n!(s-a) **1'>"38> a8> ae-cs F(s)F(s-c)F(s)G(s)s > a,s>0e-cssnF(s) - s¹-1 f(0) - f(n-1) (0)(-1)" f(n) (s)... 5+2513-¹+10+74

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Answered: 13. 5+25 s³+10s+74

Math

Advanced Math

13. 5+25 s³+10s+74

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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Question

In each of Problem 9 through 24, use the linearity of L^-1, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function:

1.
2.
f(t) = L-¹{F(s)}
1
t", n = positive integer
3.
4. t,p>-1
5.
sin at
6.
cos at
7. sinh at
8. cosh at
9. et sin bt
10. et cos bt
11. teat, n positive integer
=
12. uc(t)
13. uc(t)f(t-c)
14. et f(t)
15. Sof(t-1) g(7) dr
16. (t-c)
17. f(n) (t)
18. t" f(t)
F(s) = £{f(t)}
7,8>0
."
s > a
gm+1; 8>0
r(p+1)
8>0
ਕ, 8 > 0
+) 8>0
>
8> |a|
8> |a|
(8-4)³² +6²
8-4
(s-a)² +6²
n!
(s-a) **1'>
"
3
8> a
8> a
e-cs F(s)
F(s-c)
F(s)G(s)
s > a
,s>0
e-cs
snF(s) - s¹-1 f(0) - f(n-1) (0)
(-1)" f(n) (s)
...

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