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<A NAME=LIMIT>

<TITLE>LIMIT</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>LIMIT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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LIMITS is a fast limit package for REDUCE for functions which are 
continuous except for computable poles and singularities, based on 
some earlier work by Ian Cohen and John P. Fitch. The Truncated 
Power Series package is used for non-critical points, at which 
the value of the function is the constant term in the expansion 
around that point. l'Hopital's rule is used in critical cases, 
with preprocessing of 1-1 forms and reformatting of product forms 
in order to apply l'Hopital's rule. A limited amount of bounded 
arithmetic is also employed where applicable. 
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 <P> <H3> 
syntax: </H3>
<em>limit</em>(&lt;expr&gt;,&lt;var&gt;,&lt;limpoint&gt;) or 
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<em>limit!+</em>(&lt;expr&gt;,&lt;var&gt;,&lt;limpoint&gt;) or 
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<em>limit!-</em>(&lt;expr&gt;,&lt;var&gt;,&lt;limpoint&gt;) 
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where &lt;expr&gt; is an expression depending of the variable &lt;var&gt; 
(a 
<A HREF=r37_0002.html>kernel</A>) and &lt;limpoint&gt; is the limit point. 
If the limit depends upon the direction of approach to the &lt;limpoint&gt;, 
the operators <em>limit!+</em> and <em>limit!-</em> may be used. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
limit(x*cot(x),x,0);

  0


limit((2x+5)/(3x-2),x,infinity);

  2
  --
  3

</TT></PRE><P>