(maxima.info)Functions and Variables for Limits

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17.1 Functions and Variables for Limits
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 -- Option variable: lhospitallim
     Default value: 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
          limit (<expr>, <x>, <val>, <dir>)
          limit (<expr>, <x>, <val>)
          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).

     'infinity' (complex infinity) is returned when the limit of the
     absolute value of the expression is positive infinity, but the
     limit of the expression itself is not positive infinity or negative
     infinity.  This includes cases where the limit of the complex
     argument is a constant, as in 'limit(log(x), x, minf)', cases where
     the complex argument oscillates, as in 'limit((-2)^x, x, inf)', and
     cases where the complex argument is different for either side of a
     two-sided limit, as in 'limit(1/x, x, 0)' and 'limit(log(x), x,
     0)'.

     '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.

 -- 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
          tlimit (<expr>, <x>, <val>, <dir>)
          tlimit (<expr>, <x>, <val>)
          tlimit (<expr>)

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

 -- 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.