`Limit(f(x), For(x, a), P(x))`rendered as $\lim_{x \to a,\,P(x)} f(x)$ represents the limiting value of $f(x)$ for every sequence of $x$ satisfying $P(x)$ and approaching the limit point $a$.

If the predicate $P(x)$
is omitted, the expression renders correctly to LaTeX, but this form should be avoided since it is ambiguous whether it denotes a sequence limit, real limit or complex limit (or some other kind of limit). It is better to use

`SequenceLimit`,`RealLimit`,`LeftLimit`,`RightLimit`or`ComplexLimit`.The limit is always a deleted limit. That is, the value of $f(a)$
does not need to be equal to the limit and does not even need to be defined.

The expression

`f(x)`is not required to be defined for all $x$ satisfying $P(x)$. It only needs to be defined for all $x$ in some neighborhood of the limit point and also satisfying $P(x)$.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 |
---|---|---|

Limit | $\lim_{x \to a} f(x)$ | Limiting value |

SequenceLimit | $\lim_{n \to a} f(n)$ | Limiting value of sequence |

RealLimit | $\lim_{x \to a} f(x)$ | Limiting value, real variable |

LeftLimit | $\lim_{x \to {a}^{-}} f(x)$ | Limiting value, from the left |

RightLimit | $\lim_{x \to {a}^{+}} f(x)$ | Limiting value, from the right |

ComplexLimit | $\lim_{z \to a} f(z)$ | Limiting value, complex variable |

Source code for this entry:

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