Solve Simple Residue Question with Laplace Transforms | Limit as p->0

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TDJHOLDER
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Hi guys,

I'm doing some Laplace transforms
Apologies for not typing this out very well I don't know LaTex...
where (1/p)((sinh(p^1/2)(1-x))/(sinh(p^1/2)))

I need to work out the residue at p=0...

It's been a while since I did this but you multiply through by p and then take the limit as p->0

I can't seem to work the last bit out as the bottom of the fraction becomes zero.

I'm guessing the residue is probably (1-x) but I don't know how to get there.

Thanks in advance.
 

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