Fungrim entry: c8a5f0

Symbol: LeftLimit —

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

— Limiting value, from the left

This operator can be called with three or four arguments.

LeftLimit(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(Neg(Infinity), a))).

LeftLimit(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(Neg(Infinity), a)), 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
`LeftLimit`	$\lim_{x \to {a}^{-}} f(x)$	Limiting value, from the left
`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("c8a5f0"),
    SymbolDefinition(LeftLimit, LeftLimit(f(x), For(x, a)), "Limiting value, from the left"),
    Description("This operator can be called with three or four arguments."),
    Description(SourceForm(LeftLimit(f(x), For(x, a))), ", rendered as", LeftLimit(f(x), For(x, a)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), Element(x, OpenInterval(Neg(Infinity), a)))), "."),
    Description(SourceForm(LeftLimit(f(x), For(x, a), P(x))), ", rendered as", LeftLimit(f(x), For(x, a), P(x)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), And(Element(x, OpenInterval(Neg(Infinity), a)), 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