d. sin3t cos3t e. -4t3 + 16t + 9

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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ChapterA: Appendix
SectionA.7: Quadratic Functions And Complex Numbers
Problem 8P
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Use the Table of Laplace Transform to find the Laplace Transform of the 
given function

d. sin3t cos3t
e. -4t3 + 16t + 9
Transcribed Image Text:d. sin3t cos3t e. -4t3 + 16t + 9
TABLE OF COMMON LAPLACE TRANSFORMS
f(x)
1
F(s) = L{F(x)}
- (s > 0)
z (s > 0)
(п — 1)!
xn-1 (n = 1,2....)
(s > 0)
sn
ear
(s > 0)
S- a
a
sin ax
(s > 0)
s² + a²
cos ax
(s > 0)
s²+ a²
2as
x sin ax
(s > 0)
(s2 + a²)²
x cos ax
s² – a²
(s > 0)
(s² + a²)²
(п — 1)!
(s > a)
(s – a)"
хn+1 еах (п %3 1,2,...)
n
ebx sin ax
a
(s > b)
(s – b)² + a²
s - b
(s – b)² + a²
ebx
Cos ax
(s > b)
Transcribed Image Text:TABLE OF COMMON LAPLACE TRANSFORMS f(x) 1 F(s) = L{F(x)} - (s > 0) z (s > 0) (п — 1)! xn-1 (n = 1,2....) (s > 0) sn ear (s > 0) S- a a sin ax (s > 0) s² + a² cos ax (s > 0) s²+ a² 2as x sin ax (s > 0) (s2 + a²)² x cos ax s² – a² (s > 0) (s² + a²)² (п — 1)! (s > a) (s – a)" хn+1 еах (п %3 1,2,...) n ebx sin ax a (s > b) (s – b)² + a² s - b (s – b)² + a² ebx Cos ax (s > b)
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