https://mathwiki.cs.ut.ee/ 2026-05-22T12:22:29+00:00 https://mathwiki.cs.ut.ee/ https://mathwiki.cs.ut.ee/lib/exe/fetch.php?media=wiki:dokuwiki.svg text/html 2014-12-12T19:37:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://mathwiki.cs.ut.ee/doku.php?id=limit:limit&rev=1418413078&do=diff Limit Let $f$ be a real-valued function defined on some subset of the real line $\mathbb R$. Informally speaking, a number $c$ is said to be the limit of $f$ in the process $x \to \infty$ if $f(x)$ comes arbitrarily close to $c$ as $x$ gets larger and larger. The precise definition of limit is as follows:$c \in \mathbb R$$\epsilon$$N$$x > N$$|f(x)-c| < \epsilon$$x$$\lim_{x \to \infty} f(x) = c$$c$$f$$x \to \infty$$M$$N$$x > N$$f(x) > M$$x \to \infty$$\lim_{x \to \infty} f(x) = \infty$$M$$N$$x >…