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18.1 Definitions for Limits |

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__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`

When

`tlimswitch`

is`true`

, it causes the limit package to use Taylor series when possible.

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