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<H1><A NAME="SEC56" HREF="maxima_toc.html#TOC56">Limits</A></H1>
<H2><A NAME="SEC57" HREF="maxima_toc.html#TOC57">Definitions for Limits</A></H2>
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<DT><U>Variable:</U> <B>LHOSPITALLIM</B>
<DD><A NAME="IDX462"></A> default: [4] - the maximum number of times L'Hospital's
rule is used in LIMIT. This prevents infinite looping in cases like
LIMIT(COT(X)/CSC(X),X,0).
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<DT><U>Function:</U> <B>LIMIT</B> <I>(exp, var, val, dir)</I>
<DD><A NAME="IDX463"></A>finds the limit of exp as the real variable
var approaches the value val from the direction dir. Dir may have the
value PLUS for a limit from above, MINUS for a limit from below, or
may be omitted (implying a two-sided limit is to be computed). For
the method see Wang, P., "Evaluation of Definite Integrals by Symbolic
Manipulation" - Ph.D. Thesis - MAC TR-92 October 1971. LIMIT uses the
following special symbols: INF (positive infinity) and MINF (negative
infinity). On output it may also use UND (undefined), IND (indefinite
but bounded) and INFINITY (complex infinity).
LHOSPITALLIM[4] is the maximum number of times L'Hospital's rule
is used in LIMIT. This prevents infinite looping in cases like
LIMIT(COT(X)/CSC(X),X,0).
TLIMSWITCH[FALSE] when true will cause the limit package to use
Taylor series when possible.
LIMSUBST[FALSE] prevents LIMIT from attempting substitutions on
unknown forms. This is to avoid bugs like LIMIT(F(N)/F(N+1),N,INF);
giving 1. Setting LIMSUBST to TRUE will allow such substitutions.
Since LIMIT is often called upon to simplify constant expressions,
for example, INF-1, LIMIT may be used in such cases with only one
argument, e.g. LIMIT(INF-1);
Do EXAMPLE(LIMIT); for examples.
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<DT><U>Function:</U> <B>TLIMIT</B> <I>(exp,var,val,dir)</I>
<DD><A NAME="IDX464"></A>is just the function LIMIT with TLIMSWITCH
set to TRUE.
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<DT><U>Variable:</U> <B>TLIMSWITCH</B>
<DD><A NAME="IDX465"></A> default: [FALSE] - if true will cause the limit package to
use Taylor series when possible.
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