18. Limits

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18.1 Definitions for Limits

Option variable: lhospitallim

Default: 4

lhospitallim 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).

Function: limit (expr, x, val, dir)

Function: limit (expr, x, val)

Function: limit (expr)

Computes the limit of expr as the real variable x 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).

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 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 when true will cause the limit package to use Taylor series when possible.

limsubst 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.

limit with one argument is often called upon to simplify constant expressions, for example, limit (inf-1).

example (limit) displays some examples.

For the method see Wang, P., "Evaluation of Definite Integrals by Symbolic Manipulation", Ph.D. thesis, MAC TR-92, October 1971.

Option variable: limsubst: default value: 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.

Function: tlimit (expr, x, val, dir)
Function: tlimit (expr, x, val)
Function: tlimit (expr): Returns limit with tlimswitch set to true.

Option variable: tlimswitch

Default value: false