Category:Limit of Constant Function

This category contains pages concerning Limit of Constant Function:

Two-Sided Limit at Real Number

Let $a, b \in \R$.

Define $f : \R \to \R$ by:

$\map f x = a$ for each $x \in \R$.

Then:

$\ds \lim_{x \mathop \to b} \map f x = a$

where $\ds \lim_{x \mathop \to b}$ denotes the limit as $x \to b$.

Limit at $+\infty$

Let $a, b \in \R$.

Define $f : \R \to \R$ by:

$\map f x = a$ for each $x \in \R$.

Then:

$\ds \lim_{x \mathop \to \infty} \map f x = a$

where $\ds \lim_{x \mathop \to \infty}$ denotes the limit at $+\infty$.

Limit at $-\infty$

Let $a, b \in \R$.

Define $f : \R \to \R$ by:

$\map f x = a$ for each $x \in \R$.

Then:

$\ds \lim_{x \mathop \to -\infty} \map f x = a$

where $\ds \lim_{x \mathop \to -\infty}$ denotes the limit at $-\infty$.