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Re: Limit doesn't work properly

> Hello,
> Mathematica doesn't find the correct result as a number (1/e) of the
> following sequence:
>   a[v_]:=v!/v^v;
>   N[Limit[a[v+1]/a[v],v->Identity];
> What is the reason for this circumstance ??
> Alex

When you evaluate this limit, you should get warning messages about the
essential singularity.  The built-in Limit function is based primarily
on power series expansions, and so is not currently programmed to
handle limits at essential singularities.

The algorithm used by the Calculus`Limit` package is designed to handle
limits at essential singularities:

In[1]:= a[v_]:=v!/v^v

In[2]:= << Calculus`Limit`

In[3]:= Limit[a[v+1]/a[v],v->Infinity]

Out[3]= -

As has already been discussed in a separate thread, the Calculus`Limit`
package is not designed for general use, as it has a number of known
deficiences (which is the main reason that it is not the default
function). It is included because it happens to be useful for certain
limits, such as this one, that are not handled by the built-in Limit

The best of both functions will probably be incorporated into the same
function for a future version of Mathematica.

Dave Withoff
Wolfram Research

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