Limit of Constant Function
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Theorem
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 $-\infty$.