@c end concepts Limits
@menu
* Definitions for Limits::
@end menu
@node Definitions for Limits, , Limits, Limits
@section Definitions for Limits
@c @node LHOSPITALLIM
@c @unnumberedsec phony
@defvar 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).
@end defvar
@c @node LIMIT
@c @unnumberedsec phony
@defun 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 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.
@end defun
@c @node TLIMIT
@c @unnumberedsec phony
@defun TLIMIT (exp,var,val,dir)
is just the function LIMIT with TLIMSWITCH
set to TRUE.
@end defun
@c @node TLIMSWITCH
@c @unnumberedsec phony
@defvar TLIMSWITCH
default: [FALSE] - if true will cause the limit package to
use Taylor series when possible.
@end defvar