NUMERICAL CALCULUS PACKAGE SYMBOL

# NLimit

numerically finds the limiting value of expr as z approaches .

## DetailsDetails

• 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:
•  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 is given by the complex number d. The default setting 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:
•  EulerSum converts sequence to a sum and uses EulerSum SequenceLimit uses 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Find the limit at zero:

 Out[2]=

Find the limit at infinity:

 Out[2]=