use the definition and properties of the laplace transform to compute the laplace transform of the following function.
a. f(x)=3
b. f(x)=e的2x次方
c. f(x)=sin2x
d. f(x)=coshx
please steps by steps!
Basic formula:
L{1}= 1/s
L{sin(ax)}= a/(s^2+a^2)
L{cos(ax)}= s/(s^2+a^2)
L{e^(ax)}= 1/(s-a)
L{cosh(ax)}= s/(s^2-a^2)
so that,
a. L{3}= 3/s
b. L{e^(2x)}= 1/(s-2)
c. L{sin(2x)}= 2/(s^2+4)
d. L{cosh(x)}= s/(s^2-1)
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Verified answer
Basic formula:
L{1}= 1/s
L{sin(ax)}= a/(s^2+a^2)
L{cos(ax)}= s/(s^2+a^2)
L{e^(ax)}= 1/(s-a)
L{cosh(ax)}= s/(s^2-a^2)
so that,
a. L{3}= 3/s
b. L{e^(2x)}= 1/(s-2)
c. L{sin(2x)}= 2/(s^2+4)
d. L{cosh(x)}= s/(s^2-1)