# Calculate the range of S using Laplace Transform

1. Oct 23, 2013

### DODGEVIPER13

1. The problem statement, all variables and given/known data
find the range of values for s: f(t)=e^(-t/2)u(t)

2. Relevant equations

3. The attempt at a solution
what I did initially was to take the integral from 0 to infinity of e^(-st)e^(-t/2)u(t) dt this gave me 2/(2s+1) which when I sub in -.5 to find a divide by 0 or discontinuity then s>-.5. Then I realizeed I could do it by using the laplace transform chart so the transform of e^(-t/2)u(t) which gives s+(1/2) which gives (2s+1)/2 this is backwards from what I found earlier? I dont understand how the integral can be different from the transform but anyways if I plug in a negative .5 I would get 0 which would not be a discontinuity so it appears this way wouldnt work hmm any sugestions?

2. Oct 23, 2013

### Staff: Mentor

I think you should check your transform table again. The entry for exponential decay should be of the form $\frac{1}{s + \alpha}$