Proceeding in 'trivial' way, if ...

(1)

... You can compute...

(2)

What you are searching however is...

... and this limit is 1 only if is continuos in . A way to meet that is to find an explicit expression for , what I will try to do now... lets hope with success! ...

We start by defining...

(3)

... and then we compute [using a textbook for saving time...] the LT of ...

(4)

... where is the socalled Integralexponential Function defined as...

(5)

The next step is the computation of the LT of using the formula...

(6)

Because is...

(7)

... we obtain...

(8)

Combining (1) and (8) computed for we finally obtain...

(9)

The 'experts' of MHF are kindly pleased to control the computation, because the 'old wolf' has lost most of his teeth ... if computation is correct the next step is computing the limit for of (9)...

Kind regards

P.S. : I had to drastically modify the post in order to correct many mistakes... very sorry!...