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
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 LHospitals 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.
limit from attempting substitutions on unknown forms. This is to avoid bugs like
limit (f(n)/f(n+1), n, inf) giving 1. Setting
true will allow such substitutions.
limit with one argument is often called upon to simplify constant expressions, for example,
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.
There are also some inexact matches for
?? limit to see them.
(%o1) true (%i2)