Fungrim entry: afd5ca

Symbol: RightLimit —

\lim_{x \to {a}^{+}} f(x)

— Limiting value, from the right

This operator can be called with three or four arguments.

RightLimit(f(x), For(x, a)), rendered as

\lim_{x \to {a}^{+}} f(x)

, is equivalent to Limit(f(x), For(x, a), Element(x, OpenInterval(a, Infinity))).

RightLimit(f(x), For(x, a), P(x)), rendered as

\lim_{x \to {a}^{+},\,P(x)} f(x)

, is equivalent to Limit(f(x), For(x, a), And(Element(x, OpenInterval(a, Infinity)), P(x))).

The expression For(x, a) declares x as a locally bound variable within the scope of the arguments to this operator.

Definitions:

Fungrim symbol	Notation	Short description
`RightLimit`	$\lim_{x \to {a}^{+}} f(x)$	Limiting value, from the right
`Limit`	$\lim_{x \to a} f(x)$	Limiting value
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("afd5ca"),
    SymbolDefinition(RightLimit, RightLimit(f(x), For(x, a)), "Limiting value, from the right"),
    Description("This operator can be called with three or four arguments."),
    Description(SourceForm(RightLimit(f(x), For(x, a))), ", rendered as", RightLimit(f(x), For(x, a)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), Element(x, OpenInterval(a, Infinity)))), "."),
    Description(SourceForm(RightLimit(f(x), For(x, a), P(x))), ", rendered as", RightLimit(f(x), For(x, a), P(x)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), And(Element(x, OpenInterval(a, Infinity)), P(x)))), "."),
    Description("The expression", SourceForm(For(x, a)), "declares", SourceForm(x), "as a locally bound variable within the scope of the arguments to this operator."))

Topics using this entry

Operators