NLimit


numerically finds the limiting value of expr as z approaches .

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  • To use , you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
  • The expression expr must be numeric when its argument z is numeric.
  • constructs a sequence of values that approach the point and uses extrapolation to find the limit.
  • is unable to recognize small numbers that should in fact be zero. Chop may be needed to eliminate these spurious residuals.
  • often fails when the limit has a power law approach to infinity.
  • The following options can be given:
  • WorkingPrecisionMachinePrecisionprecision to use in internal computations
    DirectionAutomaticvector giving the direction of approach
    Scale1initial step size in the sequence of steps
    Terms7number of terms used to evaluate the limit
    MethodEulerSumthe method used to evaluate the result
    WynnDegree1degree used in Wynn's epsilon algorithm
  • The option Direction->d specifies that the approach vector to a finite limit point is given by the complex number d. The default setting Direction->Automatic is equivalent to Direction->-1, and computes the limit as z approaches from larger values.
  • approaches infinite limit points on a ray from the origin.
  • The option Scale specifies the initial step in the constructed sequence.
  • For finite limit points , the initial step is a distance Scale away from . For infinite limit points, the initial step is a distance Scale away from the origin.
  • The accuracy of the result is generally improved by increasing the number of terms, although increased WorkingPrecision will also usually be necessary.
  • Possible settings for Method include:
  • EulerSumconverts sequence to a sum and uses EulerSum
    SequenceLimituses on constructed sequence
  • The option specifies the number of iterations of Wynn's epsilon algorithm to be used by . In general, there must be at least terms for iterations.
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