Comment #3 on issue 2131 by [email protected]: failing limit
http://code.google.com/p/sympy/issues/detail?id=2131

In original expression there was division by "x".
So, instead "In [8]" must be:

In [9]: (_/x).limit(x, 0)
Out[9]: nan

That is, there is no self-contradiction.

In [10]: (diff(x**3*sin(1/x), x) / x).cancel()
Out[10]: -cos(1/x) + 3*x*sin(1/x)

The limit in this point does not exist indeed. (due to the cos() term )

Essential singularity exist only: [-1, +1].

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