finds the limiting value of expr when x approaches x0.

Details and Options

  • Limit[expr,x->x0,Direction->1] computes the limit as x approaches x0 from smaller values. Limit[expr,x->x0,Direction->-1] computes the limit as x approaches x0 from larger values.
  • Limit returns Interval objects to represent ranges of possible values, for example at essential singularities.
  • Limit returns unevaluated when it encounters functions about which it has no specific information. Limit therefore by default makes no explicit assumptions about symbolic functions.
  • Assumptions can be specified as a setting for the option Assumptions.
  • Limit[expr,x->x0] uses the setting Direction->Automatic, which determines the direction from assumptions that have been given, using Direction->-1 as the default. For limit points at infinity, the direction is determined from the direction of the infinity.


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Basic Examples  (1)

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Scope  (6)

Generalizations & Extensions  (1)

Options  (7)

Applications  (5)

Properties & Relations  (2)

Possible Issues  (2)

Neat Examples  (1)

See Also

Series  Residue  Derivative  Assumptions  DiracDelta  PrincipalValue


Introduced in 1988
| Updated in 2003