# RationalFunctionLimitPackage R¶

Computation of limits for rational functions.

complexLimit: (Fraction Polynomial R, Equation Fraction Polynomial R) -> OnePointCompletion Fraction Polynomial R

`complexLimit(f(x), x = a)` computes the complex limit of `f` as its argument `x` approaches `a`.

complexLimit: (Fraction Polynomial R, Equation OnePointCompletion Polynomial R) -> OnePointCompletion Fraction Polynomial R

`complexLimit(f(x), x = a)` computes the complex limit of `f` as its argument `x` approaches `a`.

limit: (Fraction Polynomial R, Equation Fraction Polynomial R) -> Union(OrderedCompletion Fraction Polynomial R, Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial R, failed), rightHandLimit: Union(OrderedCompletion Fraction Polynomial R, failed)), failed)

`limit(f(x), x = a)` computes the real two-sided limit of `f` as its argument `x` approaches `a`.

limit: (Fraction Polynomial R, Equation Fraction Polynomial R, String) -> Union(OrderedCompletion Fraction Polynomial R, failed)

`limit(f(x),x,a,"left")` computes the real limit of `f` as its argument `x` approaches `a` from the left; limit(`f`(`x`),`x`,a,”right”) computes the corresponding limit as `x` approaches `a` from the right.

limit: (Fraction Polynomial R, Equation OrderedCompletion Polynomial R) -> Union(OrderedCompletion Fraction Polynomial R, Record(leftHandLimit: Union(OrderedCompletion Fraction Polynomial R, failed), rightHandLimit: Union(OrderedCompletion Fraction Polynomial R, failed)), failed)

`limit(f(x), x = a)` computes the real two-sided limit of `f` as its argument `x` approaches `a`.