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Limit

  • Limit[ expr , x -> ] finds the limiting value of expr when x approaches .
  • Example: Limit[Sin[x]/x, x->0].
  • Limit[ expr , x -> , Direction -> 1] computes the limit as approaches from smaller values. Limit[ expr , x -> , Direction -> -1] computes the limit as approaches 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 makes no explicit assumptions about symbolic functions.
  • See the Mathematica book: Section 1.5.10Section 3.6.8.
  • See also: Series, Residue.
  • Related package: NumericalMath`NLimit`.

    Further Examples

    This gives the limit of a symbolic expression.

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    This gives the limit of the tangent function at approaching from the right.

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    Here is the limit approaching from the left.

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    Here is a symbolic polynomial in x.

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    This gives a symbolic limit assuming the function fn to be an analytic function.

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    If you do not use Analytic -> True, L'Hopital's rule will not be used and the limit cannot be evaluated.

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