18. Limits

18.1 Functions and Variables 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).

·

@ref{Category: Limits}

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 allow the limit command to use Taylor series expansion when necessary.

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.

·

@ref{Category: Limits}

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.

·

@ref{Category: Limits}

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

Function: tlimit (expr, x, val)

Function: tlimit (expr)

Take the limit of the Taylor series expansion of expr in x at val from direction dir.

·

@ref{Category: Limits}

Option variable: tlimswitch

Default value: true

When tlimswitch is true, the limit command will use a Taylor series expansion if the limit of the input expression cannot be computed directly. This allows evaluation of limits such as limit(x/(x-1)-1/log(x),x,1,plus). When tlimswitch is false and the limit of input expression cannot be computed directly, limit will return an unevaluated limit expression.

·

@ref{Category: Limits}

This document was generated by root on July, 13 2009 using texi2html 1.76.