Maxima Function
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).
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.