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 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.

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