11

I would like to write this kind of limit and I found a sloppy way to do it, but does anybody know a simpler way of writing this?

\documentclass{article}

\usepackage{amsmath}
\usepackage{amsfonts}

\newcommand*{\bfrac}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}

\begin{document}


                $${\lim_{\bfrac{x\to a}{<}}{f(x)}} \text{ and } {\lim_{\bfrac{x\to a}{>}}{f(x)}}$$

\end{document}

Limits

  • 4
    Please clarify the intended meaning of the two types of limits. Are you maybe looking to express the idea that the limit is taken as x approaches a from either below or above? Please advise. – Mico Dec 1 '19 at 20:36
14

I'd define suitable commands:

\documentclass{article}
\usepackage{amsmath}

\newcommand\gto{\underset{>}{\to}}
\newcommand\lto{\underset{<}{\to}}

\begin{document}

\[
\lim_{x\lto a} f(x)
\text{ and }
\lim_{x\gto a} f(x)
\]

\end{document}

enter image description here

Side note. You seem to abound with braces. Avoid it.

  • Thank you for the response, I'm pretty new to this. – robbestephan Dec 1 '19 at 21:47
  • And thank you for the braces tip, I have taken out half of them and nothing changed to de document. – robbestephan Dec 1 '19 at 21:58
13

In addition to upright arrows and greater- and less-than signs below the arrow, the left- and right-hand limits are, according to the Wikipedia article, sometimes denoted with:

  • a superscript plus or minus sign:

    \documentclass{article}
    \usepackage{amsmath}
    \begin{document}
    \[ \lim_{x\to a^{+}} f(x) \text{ and } \lim_{x\to a^{-}} f(x) \]
    \end{document}
    

    enter image description here

  • a slanted arrow (\nearrow and \searrow):

    \documentclass{article}
    \usepackage{amsmath}
    \begin{document}
    \[ \lim_{x\nearrow a} f(x) \text{ and } \lim_{x\searrow a} f(x) \]
    \end{document}
    

    enter image description here

  • 4
    second code block is the same as the first. – Scott Seidman Dec 2 '19 at 14:03
  • @ScottSeidman sorry, I was daydreaming – L. F. Dec 3 '19 at 10:07
7

I will assume that you're looking to express the notion of taking the limit of f(x) as x approaches a either from below or from above. If this assumption is correct, I believe it's quite common to use \uparrow and \downarrow instead of \rightarrow (also known as \to) to express the "one-sidedness" of the limit being taken.

enter image description here

\documentclass{article}
\usepackage{amsmath} % for '\text' macro
\begin{document}
\[
\lim_{x\uparrow a}f(x) \text{ and } \lim_{x\downarrow a}f(x)
\]
\end{document}
  • I ment left- and right hand limits. I forgot to mention that. – robbestephan Dec 1 '19 at 21:49

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