Laplace transforms for which value of s?

[Haku]

Homework Statement

In each case, state the values of s for which the
Laplace transform exists.

Relevant Equations

Laplace transform

I was wondering how you work out what values of s a Laplace transform exists? And what it actually means? The example given in class is an easy one and asks to calculate the Laplace transform of 3, = 3 * Laplace transform of 1 = 3 * 1/s. Showing this via the definition, where does the range of s come out of? I.e. how can I define when the Laplace transform of 3 = 3/s?
And what happens outside that range?
Thanks.

 

[anuttarasammyak]

I do not read the original question so as a general observation, s>0 because factor $e^{-st}$ in Laplace integral should diminish for large t>0.

 

[vela]

Take a look at http://fourier.eng.hmc.edu/e101/lectures/Laplace_Transform/node3.html.