Find the Laplace Transform of the function f(t) = e^{at}

Kye 2020-11-29 Answered
Find the Laplace Transform of the function
f(t)=eat
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Expert Answer

2abehn
Answered 2020-11-30 Author has 88 answers
Step 1
We have to find the Laplace transform of the function f(t) = e^(at)
we also know that
F(s)=L{f(t)}
Step 2
doing the transforms we get
F(s)=L{f(t)}
=L{eat}
=0esteatdt
=limr0rest+atdt
=limr0re(as)tdt
=limr|e(as)t(as)|0r
=e(as)(as)e(as)0(as)
=1(as)
=1(sa)
Step 3
Laplace Transform of the function f(t)=eat is 1(sa)
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