NLimit

• 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:

• 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 Direction->Automatic 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:

• 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.