[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

# 18. Limits

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

## 18.1 Definitions 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)`.

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.

 [ << ] [ >> ] [Top] [Contents] [Index] [ ? ]

This document was generated on March, 19 2006 using texi2html 1.76.