No, it is not. But in your case, the evaluation of your function in zero is NOT DEFINED, it DOES NOT EXIST, axiomatically speaking.
REP:Ok .. so In maths zero does not exist for that function..but the limit to zero exists.
In reality Physics claims that there is nothing called as limit to zero(in general).
And so we have a 'touch-me-not' process in Maths for which there is no equivalent analogy in Reality...But I belive that any intermediate state of the derivation in Maths is as true as the intial state (or the segregated state) and therefore the process must describe the real truth...If it is not so then Maths is not logically true to itself..(atleast to its boolean branch)
This applies to complex number based derivations also...
We need to find the Physical equivalent or else the Maths crashes... ans this is how MATHS SHOULD DICTATE...Infact it has no choice..

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Once again, since when does math describe the physical reality? And no, math uses the concept of limit to define also functions like the tangent to a curve, to calculate areas and volumes, and so on and so forth.
REP: Maths does not describe the reality but it conatins logically consistent tools which are found applicable in the Physics.
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In within limits. As I said, and I am stressing this again, mathematics is only a tool, and as such it is applied within certain ranges of validity. What matters is only the meaning of the mathematical symbols, and physics assumes its right to use math as it sees fit, and within limits that are not mathematical in nature.
REP: You are free to reduce the physical validity of mathematical concepts which are not applied to PHysics but you can not do that with concepts which are applied..(infact the interpretation extra information can go on to show that how reality can be enriched by Maths..)
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It has a meaning only to you, and maybe the Pythagoreic school, but not to any physicist. The concept of infinitesimal is very clear in classical physics, the concept of a limit is also very clear in physics, but no one makes the claim that the mathematical description should be consistent with reality in all the cases. That?s why there is something called classical physics, using one sort of math, quantum physics, using a different math, and so on and so forth.
REP: Maths must remain consistent with itself if not Physics.
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For the last time now, your function is NOT DEFINED at x=0. As such, it does not exist at that point and mathematical logic tells you that you cannot have any type of knowledge, complete or incomplete, about something that does not exist.
Ok ... fine .
Fucntion is not defined and I can not claim anything more because I am with the Reality.
We can use complex nos. now for convinience but it provides another domain of 'incomprehensibity' in Physics or reality...
Taking a Square root of -1 has survived the cruel neglect of Maths becuase it has many more useful properties than a infinity.
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Well, you used the wrong tool. The wrong representation for your function. As I said before, if you take the arctg of your function, you singularity disappears.
REP:I have droped that function now as I can use my trick to make a complex number real!!!
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dkv: I also need to revisit this thought..
Once again, be my guest.
REP: When ??:-))
I am not getting enough time right now as there are deadlines to meet.But I hope I have been able to communicate the core issue.
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It does not meet reality in full force, as you say it. But this is no problem. Physics only uses what considers necessary and how it considers it necessary. Physics is not dictated by the math, even though math is a very useful tool to ?speak? physics.In this view, complex numbers are just a convenient way to describe certain issues in physics.
REP:Physics does not use what is necessary but the Physicists use what is necessary.. and thats not good.
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It is not a reference point either. You cannot allow yourself to be biased in your views either as a mathematician or as a physicist.
REP: I support the truth.
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I am sorry to say this, but you are wrong. We don?t need to classify reality with respect to a reference, although may think the opposite. The definition of reality itself, even in philosophical terms, transcedes the necessity of a reference.
REP:It is not a question if I dont need it or not.. but I am afraid that this reality with respect to a reference is as true as reality with respect to 0.(whatever that means)
To me 0 is a ordinary as 1 ,2 or 3.Ofcourse in boolean algebra 0 means the mysterious NOT.
(NOT EVERYTHING is not equal to NOTHING becuase even Nothing belongs to everything)
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In your case, of course it can be removed. See above how. And it does not need to map to reality, but to a (very) small fraction of reality, namely the one that can be described by it.
REP: It was removed by introducing a new concept which remains unexplained physically .. or rather no has dared to explain it physically..
Who knows what does that concept stands for in reality.. even reality is not completely known.

In a nutshell I hope one day we will be able to map (rather understand)the INPUT, PROCESS and OUTPUT as written in physics and not in Maths.
Once Maths is applied to reality .. its every step should express the reality only (no maths there)...The derivation of TRUTH can not oscillate between Physics and Maths and may be it does not.