NumericalCalculus`
NumericalCalculus`

# NLimit

NLimit[expr,z->z0]

numerically finds the limiting value of expr as z approaches z0.

# Details

• To use NLimit, you first need to load the Numerical Calculus Package using Needs["NumericalCalculus`"].
• The expression expr must be numeric when its argument z is numeric.
• NLimit constructs a sequence of values that approach the point z0 and uses extrapolation to find the limit.
• NLimit is unable to recognize small numbers that should in fact be zero. Chop may be needed to eliminate these spurious residuals.
• NLimit often fails when the limit has a power law approach to infinity.
• The following options can be given:
•  WorkingPrecision MachinePrecision precision to use in internal computations Direction Automatic vector giving the direction of approach Scale 1 initial step size in the sequence of steps Terms 7 number of terms used to evaluate the limit Method EulerSum the method used to evaluate the result WynnDegree 1 degree used in Wynn's epsilon algorithm
• The option Direction->d specifies that the approach vector to a finite limit point z0 is given by the complex number d. The default setting is equivalent to Direction->-1, and computes the limit as z approaches z0 from larger values.
• NLimit 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 x0, the initial step is a distance Scale away from x0. 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:
•  EulerSum converts sequence to a sum and uses EulerSum SequenceLimit uses SequenceLimit on constructed sequence
• The option WynnDegree specifies the number of iterations of Wynn's epsilon algorithm to be used by SequenceLimit. In general, there must be at least terms for iterations.

# Examples

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## Basic Examples(2)

 In:= Find the limit at zero:

 In:= Out= In:= Find the limit at infinity:

 In:= Out= 