Let
$$F(s):=\frac{s}{2s-i}$$ be the Laplace transform of some $f(t)$. I have been asked to compute $f(0^+)$ assuming that this quantity, intended as limit, exists.
I thought I could apply the IVT and write
$$ \lim_{t\to 0} \, f(t) = \lim_{s\to \infty} sF(s) = \frac{s^2}{2s-i} = \infty $$
However according to wolfram alpha I should have another result: in particular, if I'm not getting wrong
$$ f(t) = \frac{\delta(t)}{2} + \frac{i}{4}\exp \bigg(\frac{it}{2}\bigg) \xrightarrow{t \to 0}\frac{i}{4} $$
What am I doing wrong?