Question

If f(t) = e^at, its Laplace Transform is given by?

(a) a ⁄ s^2+a^2

(b) √π ⁄ 2√s

(c) 1 ⁄ s-a

(d) Does not exist

This question was addressed to me in a job interview.

My doubt is from Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

Correct choice is (c) 1 ⁄ s-a

For explanation: The Laplace Transform of a functions is given by

\(L\{f(t)\}=F(s)=\int_0^{\infty}f(t)e^{-st}dt\)

Put f(t) = e^at

On solving the above integral, we obtain 1 ⁄ s-a.