Maxima Manual. Node: Definitions for Limits Limits
Limits
32.1: Definitions for Limits
 Variable: LHOSPITALLIM

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).
 Function: LIMIT
(exp, var, val, dir)

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 twosided limit is to be computed). For
the method see Wang, P., "Evaluation of Definite Integrals by Symbolic
Manipulation"  Ph.D. Thesis  MAC TR92 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, INF1, LIMIT may be used in such cases with only one
argument, e.g. LIMIT(INF1);
Do EXAMPLE(LIMIT); for examples.
 Function: TLIMIT
(exp,var,val,dir)

is just the function LIMIT with TLIMSWITCH
set to TRUE.
 Variable: TLIMSWITCH

default: [FALSE]  if true will cause the limit package to
use Taylor series when possible.
Limits
Limits