# RationalFunctionLimitPackage R¶

sign.spad line 174 [edit on github]

R: GcdDomain

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`

.